Knowing I'm recording myself can freak me out sometimes. The nice part is that you can go back and redo it, but the negative is that you can ALWAYS go back and redo it.
I mean it's your grandparents. They will be thrilled with whatever you give them, even if it's just one piece, even if notes are missed. They will be proud of you and honored to get that type of gift from you. If they know nothing of music, they will think it's awesome. If they know music well, chances are they already know you're playing level so it's not going to shock them or anything. They will be happy just that you are thinking of them.And as far as recordings go, no one will be aware of all the time and effort you put into it. You pick the piece, practice it up, record and all that, and then the listener might only listen to it once and halfway listen to it at that. That's another reason I wouldn't be hung up about little mistakes or making it perfect. If it's for yourself, that's one thing, but if it's for a quick breezy listen for someone else, don't knock yourself out too much.