Lee's text to Kinsler said: "It was great playing with you. Sorry, but see you in the World Series."
Kinsler, one of the players on hand for the special showing of the team DVD "It's Time," texted his former teammate: "Uncle. It's about time you made a decision."
Kinsler could joke with Lee because he was one of the pitcher's closest friends on the Rangers last year. He wished that the 32-year-old lefty was returning to Texas. Lee finalized a five-year, $120 million contract with the Phillies on Wednesday.
"I'm happy for the guy," Kinsler said. "It's disappointing that he's not going to be wearing a Rangers uniform next year. But that's the great thing about free agency. He's earned that right and he's at a place that he obviously wanted to be at."
Kinsler said Lee will certainly be missed.
"With him compared to without him is a big difference," Kinsler said. "But we have a lot of young players that are very capable of filling that spot. A lot of those guys need to grow up quicker than maybe if we had Cliff. But we have guys with a lot of talent and a lot of guys that want to be in that position. So they're going to get opportunities to step up. The offseason isn't over yet, so other moves might be made. But we have guys capable of filling that spot."
Rangers pitcher Tommy Hunter echoed those sentiments.
"He was a class act," Hunter said. "He takes care of the younger guys. He was a leader."
Hunter, another friend who went hunting with Lee in Arkansas while the winter meetings were going on, is looking forward to facing his former teammate during interleague play next season. The Rangers and Phillies face each other on May 20-22 in Philadelphia.
"It's hard to see him go," Hunter said Tuesday night. "He was a good guy, a good person. He took care of me. He's a good friend. I'm sure it's going to stay that way.
"We do get to play him, and I told him, 'Don't leave one over the plate if I'm throwing against you.' If he leaves one over the middle of that plate, buddy, it might be Justin Smoaked right back over his head. He started laughing and said, 'You'll be lucky if you get a foul tip.'"
Lee turned down reported bigger offers from the Rangers and New York Yankees to return to Philadelphia. He helped pitch the Phillies to the 2009 World Series before being traded to Seattle and then Texas.
"I enjoyed my time in Seattle. I enjoyed my time in Texas," Lee said Tuesday in his first public comments since news of the deal broke Monday night. "Looking back, I'm kind of glad I had the chance to go back to the World Series. I had a great time in Texas. I got to play close to home. It was a lot of fun. But now I'm back here and I'm looking forward to it."
Richard Durrett covers the Rangers for ESPNDallas.com. Information from ESPN.com's Jerry Crasnick was used in this report.