Do I have to pay H1B filing fee ($2200)?

[xgaffadi]

Consulting agency AGENCY_A sponsored my H1B visa. Tried for about six months, no project. Then I changed company (permanent job) with new H1B.
Now, AGENCY_A is asking me to pay for the H1B filing fees of $2200.
I haven't signed any paper with AGENCY_A.

I would really appreciate if somebody could tell me where do I stand. Do I have to pay back?
If they go for sueing me, what are my options.

 

[EricS]

If you have not signed anything with them, then you do not need to worry. H1 fee is employer's responsibility.
I assume they have not paid you for 6 months when they were looking for a project for you. Next time they call you to ask for H1 fee, tell them you need your pay for those 6 months else you will have to report DOL.