Story highlights Price resigned Friday amid scandal over chartered planes

Committed to reimbursing for cost of his seat

HHS hasn't said if he did so before leaving the department

Washington (CNN) The top Democrat on the House oversight committee wants to see proof that former Department of Health and Human Services Secretary Tom Price made good on his promise to reimburse American taxpayers for the expense of his travel.

Rep. Elijah Cummings sent a letter to HHS Acting Secretary Don Wright and Treasury Secretary Steven Mnuchin, asking the departments for a copy of the check or "other form of payment" by October 6. The request comes on the heels of the committee's bipartisan effort to learn more about the administration's use of non-commercial flights at taxpayer expense.

Price resigned Friday , one day after pledging to cover the cost of his seat on private planes -- roughly $52,000 -- he used for business travel. However, that amount would not cover the cost of chartering the planes in the first place.

An HHS spokesperson did not confirm if Price wrote the check before resigning, telling CNN only that "it's in the process."

Last week, the oversight committee's Republican chairman, Rep. Trey Gowdy, and Cummings sent letters to the White House and 24 federal agencies asking for information "related to senior officials' use of government-owned aircraft or private non-commercial aircraft for official and personal travel." The two lawmakers set a deadline of October 10 for those documents.