Shortly after coming home from a precision rifle training class (put on by Rifle’s Only) I decided to hit the range a few days later and review my notes of what had been taught and put it into practice. Hopefully retaining more of the great lessons learned in the class. A few rounds into alternate position shooting I pulled my bolt back only to not feel/hear the shell eject. 
Dropping the mag I quickly cycled the bolt a couple time only to find that is was not picking up the rim of the fired shell casing still in the chamber. At this point I wasn’t sure if I had a stuck case or a dirty bolt so I removed the bolt and bushed off the recessed area under the extractor. Grabbed a cleaning rod from the range and ran that down the barrel and as soon as it made contact with the spent cartridge case the case fell free. “That’s not good” I thought... Using a spent cartridge case, I inserted it into the bolt head to assess the problem. I quickly noticed the extractor was not engaging as it should. 
Fast forward to home. On closer examination I could see the extractor ring was jagged, this was when I learned I had a old style rivet extractor and the extractor ring had broken at the rivet.
This rifle is an old rifle. I bought it used with a fresh barrel installed so there is no telling how many rounds it had through it prior to it coming into my possession. I do know that I have put around 2000 rounds (+/- a couple hundred) since I purchased it a couple years ago. So don’t worry about your Remington extractors braking. It’s relatively rare.
I researched local smiths and well known smiths about replacing it for me and surprisingly it didn’t seem anyone wanted to. I did receive several recommendations to switch to an m16 or sako style but I really didn’t wish to send my bolt off and for the cost of the needed tools to replace it myself it was about one half the price compared to upgrading to a newer style. I am cheap, what can I say... So that is what I did, I ordered a Remington extractor anvil and a couple extractor kits (an extra in case I screwed something up). The following is my attempt at a DIY post on Remington rivet extractor replacement. I hope you find it useful.
First you need to strip the bolt down by removing the firing pin assembly. This simply unscrews but you must use something to pull the pin back every revolution until it is clear. They make a tool for this but a shoe string or in this case a loop of 550 para cord will work. I put my leg through the loop and applying pressure to the leg of the firing pin (this normally contacts the trigger assembly when it is in the rifle and hold it to the rear until you trip the trigger) I unscrewed it until it was removed.
Then remove the ejector. Again they make a tool for this but if you use care other things will work... like a 6 inch clamp I use for my brake jobs on my car and truck. I cut an old retired piece of brass to use to apply pressure to the ejector releasing the pressure on the roll pin that must be removed to free the ejector. I should add here you will need a good set of quality small punches.
Once free this is what you should have. A pin, ejector and spring. Set these aside where they will not be lost or bumped.
Next you need to punch out the old rivet. Use your punches of the proper size to tap this out. I have an old (jewelers maybe, I don’t know my hammers) small hammer that worked well.
Next remove the extractor ring. I bought some quality dental picks a while back for cleaning my rifles and these made quick work of removing the old extractor. Once this is removed it is a great time to thoroughly clean your bolt face and all the little holes. Below is a pic of the removed extractor.
Fast forward to home. On closer examination I could see the extractor ring was jagged, this was when I learned I had a old style rivet extractor and the extractor ring had broken at the rivet.
This rifle is an old rifle. I bought it used with a fresh barrel installed so there is no telling how many rounds it had through it prior to it coming into my possession. I do know that I have put around 2000 rounds (+/- a couple hundred) since I purchased it a couple years ago. So don’t worry about your Remington extractors braking. It’s relatively rare.
I researched local smiths and well known smiths about replacing it for me and surprisingly it didn’t seem anyone wanted to. I did receive several recommendations to switch to an m16 or sako style but I really didn’t wish to send my bolt off and for the cost of the needed tools to replace it myself it was about one half the price compared to upgrading to a newer style. I am cheap, what can I say... So that is what I did, I ordered a Remington extractor anvil and a couple extractor kits (an extra in case I screwed something up). The following is my attempt at a DIY post on Remington rivet extractor replacement. I hope you find it useful.
First you need to strip the bolt down by removing the firing pin assembly. This simply unscrews but you must use something to pull the pin back every revolution until it is clear. They make a tool for this but a shoe string or in this case a loop of 550 para cord will work. I put my leg through the loop and applying pressure to the leg of the firing pin (this normally contacts the trigger assembly when it is in the rifle and hold it to the rear until you trip the trigger) I unscrewed it until it was removed.
Then remove the ejector. Again they make a tool for this but if you use care other things will work... like a 6 inch clamp I use for my brake jobs on my car and truck. I cut an old retired piece of brass to use to apply pressure to the ejector releasing the pressure on the roll pin that must be removed to free the ejector. I should add here you will need a good set of quality small punches.
Once free this is what you should have. A pin, ejector and spring. Set these aside where they will not be lost or bumped.
Next you need to punch out the old rivet. Use your punches of the proper size to tap this out. I have an old (jewelers maybe, I don’t know my hammers) small hammer that worked well.
Next remove the extractor ring. I bought some quality dental picks a while back for cleaning my rifles and these made quick work of removing the old extractor. Once this is removed it is a great time to thoroughly clean your bolt face and all the little holes. Below is a pic of the removed extractor.
