The House Oversight Committee letter asks HUD to produce documents and communication related to redecorating the secretary's office.
Chairman Trey Gowdy asked the agency to provide all documents "To help the committee determine whether HUD adhered to the applicable spending limitations while redecorating your office" in the letter.
He wrote that HUD must provide the information by March 14 and wants officials to brief the committee.
Foster says she told Clemmensen that there was a $5,000 legal limit but he allegedly responded that the "administration has always found ways around that in the past" and told her to "find money" to purchase furniture. He allegedly said "$5,000 will not even buy a decent chair," according to the complaint.
Clemmensen did not respond to a request for comment on Tuesday.
The agency provided documents to ABC News confirming the purchase of the table in response to questions. A copy of Foster's complaint was provided to ABC News by her attorney.
Federal law regulating the use of taxpayer money says that any expense for redecorating an agency head's office more than $5,000 has to be reported to the House and Senate Appropriations Committees. The law also says that the rule applies to any money spent to redecorate the "entire suite of offices assigned to an individual" and not just the physical office.
An aide for the Senate Appropriations Committee said Wednesday that the only HUD purchase they were aware of is blinds for Carson's office that they were less than the $5,000 limit. A spokeswoman for the House Appropriations Committee said they did not receive any sort of disclosure from HUD.
A HUD spokesman said the agency won't comment on specific allegations in the complaint, but said the agency did not spend more than $5,000 to redecorate Carson's office.
HUD's communications director, Raffi Williams, said the secretary replaced the existing furniture in the office with items the agency had in storage and that the only additional expense from the decorating budget was $3,400 to buy blinds.
Carson took to Twitter Wednesday night to seemingly address the controversy, writing, "Thank you to so many who have expressed concern for me and my family over the latest accusations. Rest assured that there has been no dishonesty or wrongdoing by us. All the numbers and evidence are being gathered and a full disclosure is forthcoming."
He continued, "We suspect, based on past attempts, that they will continue to probe and make further accusations even without evidence or substantiation. We will continue to ask for God’s guidance to do what is right."
Documents provided to ABC News by HUD show that the agency spent $1,100 to try to repair the chairs in the dining set before ordering the more expensive replacement. Williams said the decision to buy the table was made by building career staff and not by the secretary.
Foster began working at HUD in 2016 and still works as the agency's chief FOIA officer.
ABC News' Ali Rogin and John Parkinson contributed to this report.