[CA] Am I f*cked?

I recently completed interviews with my dream company, and the recruiter let me know they’re moving forward with a background check - including verification of my employment history.

Here’s the issue: my resume lists the client company I’m currently working for, but I’m technically employed through a staffing agency on a contract basis. So, if they check something like The Work Number (TWN), they’ll likely see the staffing agency as my employer - not the client company.

In my defense, I’m contributing full-time to the client, working onsite with their team, and my responsibilities are identical to those of their full-time employees.

Am I in trouble? How should I handle this?