They can refuse it. The question is what do they do if you don't pay what they are asking for?
So far as I know, this is a normal civil debt. The next action most creditors would take would usually be to apply to Court for a CCJ, but I don't know whether Tax Credits operate that way. If they did, yo uwould be able to put in a financial statement to the Court, together with your payment offer. If the Court then accepted the offer and you paid it, Tax Credits could do nothing more. BUT you would have a CCJ on your Credit Ref. Agency records for 6 years, & difficulty getting credit. Do you want that?
If you have not done so, prepare a detailed financial statement showing you can't afford more than �20 (if that is the case) and send it to them to try and persuade them to accept your offer. Start paying the �20 anyway.