After restore, Time Machine thinks Mac is new computer

I've recently had problems with my Mac. Long story short, I had some troubles, and I restored my Mac from a Time Machine backup. That didn't fix a problem, but atfer the resotre, reinstalling the operating system solved it. Everything is fine, except for the fact that Time Machine doesn't think my Mac is the same as my "old" one. It correctly says the last date it was backed up was April 18th (the day I started the restore) but it is trying to back up the entire hard drive. I need it to make it recognize that this is the same Mac.