How can a request for a garnishment be reinstated?

No one can predict what a third party will do. Clearly, the third party you may owe money to has no reason to believe you will pay a debt by check if they took you to court in the first place. In any event, if the third party over collects by way of wage garnishment and a separate check you sent them, they will be required to return the amount collected above and beyond the debt.

Your question is a bit confusing because you seem to be talking about two different scenarios. Garnishments happen after a money judgment has been entered against a person. You have to sue someone first to get a money judgment. And, of course you have to win your suit. That can be because the other party doesn't defend (so you win by default) of by some sort of trial or settlement. Garnishments generally allow for a one-time taking of money (from a bank account) or for a short period of time (from paychecks, every 90 days). But the details of your question suggest you either were just sued (or are about to be sued). Or do you have an existing judgment against you? I cannot predict what a third party will do. What I can say is that if you paid the debt and are then sued you need to answer the lawsuit and show proof that you have, in fact, paid the debt. Doing nothing is the worst possible thing you can do when you are sued. I hope you kept copies of the whatever documents you sent, including the check (or can get a copy). That will help a lot.