So Spieth fired back on Sunday.
The two-time major winner said part of his preparation for this week's PGA Championship at Whistling Straits will involve a match between him and buddy Justin Thomas against Mickelson and Rickie Fowler.
"I'm going to try and get the U.S. Open trophy flown in so I can sit on the front of each green for Phil," Spieth said. "So I'll have something for him -- just dishing it back. We'll see if we can get somebody to carry it around for the round.
"It's the first time I have something on him."
Spieth, 22, won the U.S. Open at Chambers Bay in June. Mickelson, 45, has six runner-up finishes at the U.S. Open without a victory, the only major keeping him from a career Grand Slam.
After shooting a 4-under-par 66 at Firestone Country Club, Spieth was in a good frame of mind has he heads to the PGA Championship.
In each of the tournaments preceding a major championship this year, Spieth has fared well.
He lost in a playoff the week before winning the Masters, tied for third at the Memorial two weeks prior to winning the U.S. Open and won the John Deere the week before heading to St. Andrews, where he tied for fourth, a shot out of a playoff, in his bid to win the third leg of the Grand Slam.
"I think it helps a lot," Spieth said. "For the most part, guys go in streaks with the way they play throughout a year. You see guys starting to trend in the right direction, and all of a sudden, they're in contention a few weeks in a row. Then they have an off week, and then they bring it back.
"We seem to have nice timing with where we're trending upwards this year. Whether that's the plan we put in place or it is dumb luck, one of the two, I'll take it."
For the first time since the AT&T Byron Nelson Championship in May, Spieth was not in Sunday contention, his 66 getting him a tie for 10th. He finished outside of the top 10 in a tie for 30th at the Nelson. Since then, he tied for third at the Memorial, won the U.S. Open, won the John Deere and tied for fourth at The Open.
"I'm looking at it as a nice solid week, and I'll really just try and feed off of this round more than anything," Spieth said.
Spieth said he has a meeting planned Monday with his coach Cameron McCormick. Since Speith visited Whistling Straits for two days last week, he's unsure how much he will play in the coming days, aside from the 18-hole match on Tuesday.
Mickelson loves those Tuesday get-togethers and has for several years taken the younger plays under his wing for such endeavors. He's coming off a tie-for-63rd finish in which he failed to break par during any round at the WGC-Bridgestone Invitational.