H1-B Question, Please help?

I accepted a job offer last month and then my employer asked me to sign a visa repayment agreement which means that in case I leave the job before 24 months from the time the company has incurred visa costs, I will have to reimburse all those costs. My joining date is due June 6th. But now I am changing my mind to join a different company. So my question is whether the company would have incurred any costs by now. I asked them that whether they have started my visa process. They said yes, and that they are waiting for an approved LCA. Important:I have not yet provided them any of my documents like I-20, passport etc. which probably means that they would not have filed the petition yet. So do you think if I deny to join that company right now, will I have to pay them anything?