The Consumer Price Index found inflation was up on a month-to-month basis at 0.3%, but this was lower than the prior period's 0.4% and a lesser increase than some expected.

The 10-year yield was at 4.37%, down from a close of 4.45% on May 9, although it did go back up to 4.53% on May 13.. 

Lender Price data posted on the National Mortgage News website as of 11:45 a.m. had the 30-year FRM at 6.856%, compared with 7.115% one week prior.

The 30-year FRM as posted on Zillow's website as of late morning Thursday was at 6.55%, down 24 basis points from the prior week's average of 6.79%.

Recently released data on inflation and retail sales show consumers are slowing down their activities, said Orphe Divounguy, senior macroeconomist at Zillow Home Loans.

"Adding to reports of easing wage growth and dwindling consumer savings last week, this week's inflation report showed that consumer price growth is moderating," Divounguy said in a Wednesday evening statement. "Lower than expected retail sales data also pointed to a slowing economy."

That is pushing mortgage rates to their lowest level since late February.

The spring home buying season has started on a very good note, said Amy Lessinger, Remax president, in its April National Housing Report.

"Gains in home sales, new listings and the number of homes for sale are all signs of a more active, rebalancing market," said Lessinger. "This has happened without a significant drop in interest rates — suggesting that buyers and sellers may be less apt to delay their plans this year."

But Redfin, which puts out a rolling four-week report on Thursdays, noted that while new listings were up 10% from a year ago, they were flat with the prior week.

The good news was that mortgage rates, as tracked by Redfin, were under 7% for the first time in five weeks.

"Sellers know that high mortgage rates mean they should expect negotiations, expect offers to come in under list price, and be ready for some back and forth on things like repairs and closing costs," said Marsha McMahon-Jones, a Redfin agent from Palm Springs, California, in a press release. "Buyers may not be able to get a lower mortgage rate, but they're often getting homes for slightly less than the asking price."

As for the housing market and rates going forward, "Financial markets still expect at least one or two central bank rate cuts this year," Divounguy said. "Expect more rate volatility ahead as the Fed and investors wait for more conclusive evidence of a return to low, stable and more predictable inflation."

A veteran mortgage originator is also not quite ready to celebrate because of the CPI news.

"The markets are rallying and cheering because this is the next step toward the launch of a rate cut by the Fed," Melissa Cohn, regional vice president of William Raveis Mortgage, said in a statement. "It's not enough to get the Fed to cut rates."

More data points need to come out, "and there needs to be more consistency on an ongoing basis before we'll actually see the Fed cut rates," she continued.

However, Louis Navellier, an investment banker, predicted two rate cuts by the Federal Open Market Committee, with the first coming at the July 31 meeting, and the second probably in September.