You will never be part of any organisation like neither clients nor teksystems. You will be just a replaceable external employee.
There is no career growth or opportunities if you are working through them.
Hardly I have ever seen anyone getting permanent payroll of the clients org, if that's what you are thinking before joining. It's better to join any other service based company than this, and through those company you can work for any client.
If anything goes wrong no one will take stand for neither your parent company nor the client.
They might promise of allocating you to other clients if the current one removes, but that never happen.
Its just bunch of spineless HR in Teksystems who works there just to impress their client, so don't expect anything from them in terms of support.