DVD Player remote problem

I got my parents a new DVD player to replace their dying Sony. Unfortunately, looks like the DVD player and TV are operating on the same remote frequencies; navigating DVD menus brings up TV menus as well. There’s nothing we can do about this, is there?

Aren’t there some “universal” remotes? Perhaps you could replace both of them for one of them and solve this?

I don’t think that would work. I don’t know if we’re talking frequencies or what exactly on a technical level here, but whatever they are, the TV and the DVD player both react to the same ones. I don’t see how that’d be any different if the signals were coming from a universal remote or the regular ones.

That is a bit of a problem O_o