When someone offers you something and you refuse, it's polite to say "Thank you" to them for making the offer:

A: Do you want to come out with us?

B: No, I think I'll stay in tonight. Thanks for offering, though.

You use "though" at the end of a sentence to mean something similar to "but" or "however". But unlike "but" and "however", "though" can come at the end of a sentence:

I didn't really agree with the point she was trying to make. She did tell some interesting anecdotes, though.