The 20 basis point weekly gain was the largest since April, Sam Khater, Freddie Mac chief economist, said in a press release.

"However, we should remember that the rise in rates is largely due to shifts in expectations and not the underlying economy, which has been strong for most of the year," Khater continued. "Although higher rates make affordability more challenging, it shows the economic strength that should continue to support the recovery of the housing market."

The 30-year fixed rate mortgage averaged 6.32% for Oct. 10, up from 6.12% one week prior, Freddie Mac's Primary Mortgage Market Survey reported. But it was still 125 basis points lower than the 7.57% it was at for the same week last year.

At the same time, the 15-year FRM gained 16 basis points, rising to 5.41% from 5.25% as of Oct. 3. For this time last year, it was at 6.89%.

Zillow's rate tracker showed the 30-year FRM increased 19 basis points as of 11 a.m. Thursday morning, to 6.19% from last week's average of 6%.

Compared with the previous day, the rate was 4 basis points higher, with the morning's Consumer Price Index report likely being a factor.

Meanwhile, the 10-year Treasury yield continued to rise as well. It broke back above 4% at the start of the week and was at 4.1% at 11 a.m. on Thursday, up 25 basis points from its close seven days prior.

"Mortgage rates rebounded this week on stronger than anticipated employment and wage growth data," said Orphe Divounguy, senior economist at Zillow Home Loans in a Wednesday night statement. "Last week's strong jobs report caused yields and the mortgage rates that shadow them to rebound sharply."

Even before the CPI report showing inflation running hotter than expected, Divounguy said whether any further rate cuts by the Federal Open Market Committee were coming is not clear, noting Chairman Jay Powell said any future action would be dependent on incoming economic data.

"Traders are now putting the probability of a 50 basis point rate cut at the next FOMC meeting at 0%, down from 32% before the jobs report," Divounguy said. "More stubborn core inflation would likely prevent further declines in long dated yields and mortgage rates."

More volatility in mortgage rates is likely as traders parse economic data as it comes in, Divounguy said.

Despite the uncertain environment, the Mortgage Bankers Association expects rates to fluctuate between 6% and 6.5% for the next several months, Bob Broeksmit, president and CEO said in a Thursday morning comment on the Weekly Application Survey.

So another reduction in Fed Funds Rate at the next FOMC meeting remains likely.

"A higher-than-expected headline and core CPI print likely reduces the chances of a Fed rate cut in November, though a 25-basis point cut remains the baseline expectation," Sam Williamson, First American Financial senior economist said in a  statement. "Friday's [Producer Price Index] release will offer further clarity."

The latest Wolters Kluwer Blue Chip Economics Indicators survey, also conducted before the CPI report came out, raised the consensus expectations for FOMC rate cuts this year to total 94 basis points, up from 76 basis points one month prior.

While all participants expect a 25 basis point cut to be the next move out of the Fed, 98% think that will happen at the November meeting. The remaining 2% believe the FOMC will hold off until December.