The family element is the amount you get if your income is quite high & you are not therefore entitled to anything more. It is about £10.50 p wk. What happens is that, if the family element is the only amount of Tax Credit you are entitled to they remove 100% of it to go towards recovering the overpayment. This goes on every year until the overpayment has been fully recovered, PROVIDED that you continue to be entitled to the family element.
If you cease to be entitled to the family element (which is reviewed each year when your annual declaration is done) and are therefore not entitled to Tax Credits at all, they will contact you to get the money back by direct payment by you.
Tax Credits are complicated. Are you satisfied that the overpayment is your fault? If you have any doubt it would be a good idea to get someone such as your local CAB or other welfare benefits advice agency to check it.