My ass-kissing corp side shows up.
1) Is it possible the offer will be withdrawn based on your attempt to negogitiate.
2) Were you given a $$ amount for moving relo during negotiation, or did
they say, "Don't worry, We'll relocate you"?

If #1 - shut up, unless you think they are screwing you, and you can accept the OK job.
If #2 == Don't worry - shut up. You are done negotiating. You lost your leverage when you told them yes (offer letter or no, they KNOW you want the job over all others).