"I think it's extremely important. What it shows you is the dollar move we had this year is really impacting their (Fed) thinking. They haven't said that before, but they're telling you that in their forecast," said Jens Nordvig, global head of G-10 currency strategy at Nomura. "I think a lot of people were getting too relaxed about the 'Fed doesn't care about the dollar,' but the forecasts tell you they are already taking it into account a lot."
Fed officials pared back their rate hike forecasts to a slower and lower trajectory. They basically cut the midpoint expectation for 2015 in half, with a year-end rate of about 0.6 percent. The central bank also forecast inflation would slow to half its prior projection—or 0.6 to 0.8 percent for 2015. Fed officials also reduced expectations for the longer-run unemployment rate to 5 to 5.2 percent, from 5.2 to 5.5 percent.
Read MoreFed removes 'patient' but says no April hike coming
It also tweaked its growth forecast, trimming it to 2.3 to 2.7 percent for 2015 from 2.6 to 3 percent, and warned that export growth has weakened.
Nordvig said the about-face in the dollar, which had increased more than 10 percent year to date, could go on for several months. He expects a pullback "especially versus the EM currencies that have been beaten down significantly. I think this is something that could be a catalyst for a near-term turn," he said.
But strategists also expect any dollar decline to be a blip in an otherwise upward trajectory.
Read MoreDollar hammered amid Fed, euro surges past $1.10
"Everybody was tripping over themselves calling for 80 cents on the euro. It's natural for the dollar to pause here," said Boris Schlossberg, partner at BK Asset Management. "I don't think the dollar rally is over by any stretch of the imagination ... could we go close to parity? Yes, but for now I think $1.05 holds."
Fed Chair Janet Yellen noted during Wednesday's briefing that the dollar's gains were the result of a stronger U.S. economy. The Fed's steps toward tightening have been boosting the dollar at the same time other central banks, like the European Central Bank, have been easing. That has been a big factor in the euro's decline.
As expected the Fed signaled it would move to hike rates, by dropping the word "patient" out of its statement. Economists had mostly expected the first hike in June or September but that has changed.
"Essentially what's going on is June is starting to be priced out. It could be fully out. The question is are we going to have a question mark around September. ... It's not about shifting June to September," said Nordvig.
Goldman Sachs economists for instance said their forecast remains for a first hike in September, but there are now risks it could be later.
Yellen also stressed that the removal of "patient" does not mean the Fed will move soon. Instead it will rely on data, especially on jobs and inflation.
Read MoreHere's what changed in the new Fed statement
Data expected Thursday include weekly jobless claims and the current account, at 8:30 a.m. ET. The Philadelphia Fed survey and leading economic indicators are released at 10 a.m.
Traders are also watching to see whether Apple impacts trading in the Dow. It was included in the Dow 30, effective as of Wednesday's close, replacing AT&T. Dow component Visa also split 4-for-1. Other corporate news includes Lennar earnings, before the bell, and Nike earnings, after the market close.
But markets will also be focused on how the outcome of the Fed meeting shifts market expectations. Stocks jumped, with the Dow up 227 at 18,076. Bond yields moved dramatically Wednesday, with the short end of the curve seeing a big decline. The two-year was yielding 0.54 percent late in the day, moving from 0.67 percent before the Fed statement.
Read MoreUS stocks rebound on dovish Fed, with Dow topping 18K
Nordvig said his forecast for the dollar's gains this year had been relatively conservative, compared to some. Many strategists had expected parity with the euro this year, but his year-end target for the euro remains $1.05 per dollar.
"We were expecting the Fed to blink in the period before June. They're blinking earlier than we thought," he said. "It ... suggests the dollar is going to trade with a less clear global trend than we've seen."