Don't own one myself, but 3 guys at work have either Savage or the Remingtons. 3 different opinions there from them.
They're all package guns. One Savage in 7mm-08, owner loves it, has hunted moose elk and deer with it for years with no problems, still has the factory scope. He's also a firearms instructor.
Second fellow has a 770, in 7mm-08. New to hunting, wanted a low-cost entry rifle, has shot a deer with it and has no complaints so far. He's not happy with the scope, and has already arranged for Mrs. Claus to put a Bushnell 3200 under the tree.
Third fellow bought a 770 in 300 Win Mag. His first shot on a deer, the scope blew up. Literally in pieces. Took it back to Wholesale and the guy behind the counter says: "I will not put the same replacement scope on here, 'cause you're gonna be back in a day or two. I'll give you cash against a better scope instead." Still no reports on how the rifle functions.
My first deer rifle was a brand-new Savage package deal 6 years ago in 30-06. Before I shot anything other than paper targets with it, I had to put on a new recoil pad, because the tractor-tire tough 1/2 inch thick deal gave me the worst flinch of my life inside of a box of shells. Then I shot rings loose. Then I shot the ring bases loose. Then the front action screw. Nothing had been torqued right or Loc-tited. After one season, the reticle was shot loose and wouldn't hold POI from shot to shot. So it got a Bushnell 3200 and no worries since.
You get what you pay for; the less you pay the higher gamble you're making. Don't expect much out of a package gun beyond a season or two, and it sounds as though heavier calibers treat those package deal scopes like rented mules; but no problems with stuff .270 or smaller, it seems.
Hope something in there helps, but at work we have a saying: "A bad day at the range is better than the best day on post" Keep shooting, and enjoy it for what it is!