Good scopes are designed to handle recoil. Chinese stuff is a big iffy.
Quality is quality. I know for a fact that Tasco and Simmons won't always hold up to recoil. Not sure if they're "Chinese stuff" or not. Cheap scopes will work on .22s, higher power rifles deserve quality scopes.
I've had good luck with Bushnell, though. They're built rugged. Optics on the cheaper ones often suck, but that Elite is a higher end Bushell. I had a Banner on a 7 mag for quite a while before I stuck that cheap POS Simmons (cheap, well $150 you'd think it'd not be cheap, replaced an 80 dollar Bushnell that worked well
). I'll never ever give Simmons the time of day again. The Tasco was a Pro Point pistol scope on a heavy recoiling .45 Colt in a Contender. It shook the reticle out of that scope and just sorta turned black, weird. Had it repaired, lifetime warranty, and I use it now on a .30-30 barrel with compensator that doesn't recoil bad at all and it's gone a dozen years on that rig with no problems. It's a clear scope, but I know better than to use it on something that kicks, now. It held zero just fine, just the reticule came apart. I've never heard of a scope doing that before this.
I think you'll be just fine with your Bushnell Elite, though. Those are quality scopes. They don't have snob appeal like Leupolds or Ziess or the higher dollar stuff, but I have several of the cheaper ones, sportviews and banners, and they've never given me any mechanical problems. I have a little 1.5x4.5x22 that's pretty awesome, have had it on several rifles over the years. Only thing I don't like about it is the fact that it doesn't gather light real well. I have a 4x12 Banner on my .257 Roberts that's about 30 years old and never given me a problem. Not a heavy recoil, but I know a guy with the same scope on a 300 win mag that likes it. I don't really care that much for it, though, 10-12 power gets sorta fuzzy, not the greatest optics and I'm looking to put a Weaver on that gun eventually. I like Weavers a lot, rugged to the max. I don't think there's a better scope out there for the dollar. There are better scopes out there, but it takes 3-400 bucks to equal a 200 dollar Weaver IMHO.
I out shot an old boy in the club once with that .257/Bushnell. He owns nothing, but Schmidt and Bender and his rifles are a couple of Weatherbys and a Kleingunther. He was so POed, he didn't speak, just packed up and left before the shoot was over. LOL! That old Remington/Bushnell has killed a a dozen deer or better since I got the scope. Had an old steel late 50s era Weaver KV on it originally that I took a dozen or so with and I don't know how many my grandpa took with it. You don't have to have the latest $3,000 Schmidt and Bender to get the job done. Gives you braggin' rights and ultimate snobness around the campfire, but it won't kill any more deer IMHO. Oh, I've shot his guns with those S&Bs and if I had his money, I'd buy a couple, wonderful optics, needless to say, but ain't like I NEED a S&B to kill a deer, done it with iron sights after all. And, I don't target shoot or shoot prairie dogs at 10,000 yards. But, you certainly do need something that will handle recoil and it pays to stay away from the cheap stuff. I think 200 bucks and up should get the job done. I get real worried about a sub 200 dollar scope I don't know about anymore after that Simmons experience with the 7 mag. I KNOW Weaver works and they're affordable, so that's pretty much how I've settled with scopes now days. I get one on that .257, my major hunting rifles will all have decent glass on 'em. The 7 now wears a Weatherby Supreme I got a good deal on. That glass is pretty AWEsome.