It would be a good idea to simply replace the factory trigger on almost any Remington bolt gun The 700, 721, 722, 7, and 600 series all use the same trigger. I'm not certain about the 710, 770 or 783 budget rifles. The 788 is a different design. A Timney trigger is just over $100 and is a 10-15 minute DIY install.
Lots of bad stuff going on with them. The triggers made 1946-2006 are a flawed design. Statistically less than 1/2 of 1 percent will ever fail. But 100% of them could fail at any time. This isn't a manufacturing defect where a few rifles were affected. It is a design issue where certain parts inside the trigger must align perfectly and if they do the firing pin will drop with no trigger pull. Remington is not advertising it as a recall, but any of the above rifles can be sent in and have the trigger replaced free. There is a class action lawsuit still in the works to work out further details, Remington may be forced to buy them back if consumers choose to do so. But that isn't final, just one proposal that has come up.
I'm not exactly sure what is going on with the 2006-present trigger. Initial reports were that the design was sound but early rifles may have gotten adhesive in the trigger during assembly and they were recalled. But there may be more to that story too.
Rather than waste time with sending my rifle (1974 manufacture) in I simply bought a new trigger and swapped it. That is my advice to anyone who owns a Remington of any vintage.