I went through this myself at 18, when a man in his late 60s who I came into contact with regularly, couldn’t take his eyes off me. Eventually he told me that I looked remarkably like the girlfriend he hadn’t married as a young man, and it just jolted him time after time. It made me feel friendly and flattered instead of awkward. It could be a good idea to encourage grandpa to talk a bit more about his feelings, so that if nothing is wrong it doesn't matter - and of course the reverse if it is a real problem.
It is hard to know whether this is sad or horrifying. What "bad behaviour," if you don't mind my asking? How is the young lady taking it?