The message did not go over well with HUD, which took over control of the housing authority in March.
Jereon Brown, a HUD spokesman, said compliance with the latest HUD directive "is not optional."
"We have the means and the authority to withhold or recoup taxpayer dollars when the funding was spent in an inappropriate manner," Brown said.
Schnader was hired by PHA to handle a federal audit of the "housing choice voucher" program, which supplies rent subsidies to low-income families.
Adams defended Schnader's work and said each one of the hundreds of time entries on billings "are specific instances where legal advice and guidance was warranted."
She added that HUD "is being arbitrary" and must provide the "factors and criteria" for deciding that the payments to Schnader were unreasonable.
The issue of Schnader's billings is part of a far-reaching examination of PHA's legal spending during the tenure of former executive director Carl R. Greene.
Greene was fired in September 2010 after PHA's board of commissioners discovered that the agency had settled three sexual-harassment complaints against him. HUD will not return local control until the agency rebuilds its management and implements changes.
Meanwhile, in an audit in March, the HUD Inspector General called into question PHA's spending on legal services. Auditors criticized the housing authority's overreliance on outside lawyers. From 2007 until 2010, PHA spent $38.5 million on legal fees, far more than other big-city housing authorities.
HUD wants to examine all of PHA's legal bills, but the review is being held up by a court challenge from Greene. The former executive director said the release of the legal bills would violate his attorney-client privilege.
Schnader, which billed PHA for a total of $3 million during the 2007-10 period, is just one of several law firms whose billings are now being scrutinized.
