By Samantha Delouya, CNN

(CNN) — The housing market this week largely shrugged off the turmoil at the Federal Reserve.

The 30-year fixed mortgage rate averaged 6.56% for the week ending August 28, just slightly lower than last week’s 10-month low of 6.58%, according to data released Thursday by Freddie Mac.

The relatively muted move in rates comes against the backdrop of a legal clash between President Donald Trump and Fed Governor Lisa Cook. Some worry the fight could not only jeopardize the Fed’s political independence but may also lead to higher mortgage rates in the future.

On Monday, Trump announced he was firing Cook, accusing her of committing mortgage fraud. She has not been charged with any wrongdoing, and she filed a lawsuit Thursday challenging Trump’s attempt to remove her from her prominent role at the central bank.

Trump has stepped up attacks on the Fed as part of his push to drive down interest rates. But if political pressures lead the central bank to prioritize rate cuts and lose sight of controlling stubborn inflation, the strategy could ultimately backfire, Eric Hathaway, a portfolio manager at RBC Global Asset Management, told CNN.

“We are concerned about Fed independence, and we do believe that any significant loss in Fed independence will translate into higher rates,” he said.

Mortgage rates generally move in step with the 10-year Treasury yield, which the Fed can influence but doesn’t control. But the yield also reflects investors’ expectations for future inflation.

That means mortgage rates don’t always directly follow the Fed’s moves. For example, when the Fed started to cut interest rates last fall, mortgage rates rose.

For now, though, the drama at the Fed hasn’t had much effect on home borrowing rates. Mortgage rates have recently been falling as investors increasingly expect the Fed to cut interest rates in September, following weaker jobs data that points to a cooling economy.

“Right now, I don’t think that we’ve had much of a market reaction from these attacks,” Hathaway said. “But if the attacks continue and the market starts to believe that the Fed will truly lose independence, that will obviously create some concern about inflation down the road.”

On Tuesday, Trump seemed to suggest that he could replace Cook and secure a majority of his own appointees on the Fed board, enabling him to effectively ensure the central bank will bring rates down to a level he finds acceptable.

“We’ll have a majority very shortly,” Trump said at a Tuesday Cabinet meeting. “Once we have a majority, housing is going to swing and it’s going to be great. People are paying too high an interest rate… We have to get the rates down a little bit.”

Lisa Sturtevant, chief economist at Bright MLS, a real estate listing company, said that current economic uncertainty and questions about rate cuts may be creating confusion in the minds of potential home buyers who are currently sitting on the sidelines in the housing market.

“If you are a home buyer who is ready to get into the market, and you can afford to buy a home in this market, you can take advantage of more inventory and of more negotiating power than you could have a year ago,” she said. “That’s where I would focus my attention.”

“Sellers are cutting prices, inventory is lingering, so the focus on mortgage rates might, in some ways, take away from other opportunities that buyers have in the market to make the bottom line work for them,” she added.

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