I'm not sure if you saw my questions, or if you did, why you chose not to answer them. Working with an attorney is a dialogue and we ask questions because the answers are legally significant.
I'll try to answer your question, vaguely, without the information that I requested.
A contract is meant to be the single representation of the agreement between two parties. So, when you mention an offer letter (which is not a legally binding contract) and a contract requiring reimbursement for moving expenses, my concern is that the contract supersedes the offer letter. Unless the offer letter is specifically referenced in the contract, the offer letter will have no legally binding significance.
This doesn't mean that you couldn't have some recourse, but it limits the strength of the recourse. If the contract had incorporated or mentioned the offer letter, it would be very easy for you to claim breach of contract by them, so then you would not be legally held to it yourself (the doctrine of "unclean hands" we call it).
If the offer letter is NOT mentioned or incorporated into the contract, then you're left with a more difficult option. You have to allege that you have been "constructively discharged" due to the dramatic change in your compensation package. You have to approach your employer, broach this subject and explain that you will consider yourself constructively discharged and free from the contract if they do not maintain the terms under which you were led to sign the agreement. The employer has to have the opportunity to reject/accept your request (the opportunity to cure) in order for you to properly set up the constructive discharge argument.
It's not a guaranteed victory, but it is a legally viable argument on these facts.