I would refer to the purchase contract and included contingencieswhile seeking the advice of your real estate agent to get the answer to this question. This answer could vary depending on these contingencies. If the contract is contingent of the successful completion of a home inspection for any deficiencies. If the septic tank was a point of the inspection, then you would probably be required to pump it; moreover you as the seller are required to disclose the full condition of your home; you cannot keep any pertinent information about the home a secret from the buyer; so if you were aware that the septic tank needed pumping and did not disclose this to the borrower, it makes the contract voidable. On the other hand, if the borrower was aware of the condition of the tank before they entered contract and they still agreed to terms, you will not be required to have the septic pump cleared because they should have included it in their offer as a contingency.
On a side note states laws differ, so I would refer to state statute, or have your agent do it – it is their job. Depending on the state, their may be a specific statute referring to waste disposal requiring owner to empty a septic tank when property is transferred. If this was the case I would have expected your agent to go over this detail when taking the listing. If they didn’t and this is required of you, I would ask them to pay for the pumping with a credit from their commission back to you at closing to compensate for their mistake.