As a long time contractor, this is a new one on me. They should be granting YOU a 10% draw to start work not you paying them.... sounds like a signing official(s) is trying to get a piece of the pie for themselves.
I think I would not walk away .. but run!!! If this got out (that you paid graft for a job), in some overseas countries, you may NEVER return from the job site.
Just my thoughts and opinions.