"We handle our stuff in-house," Gase said Friday. "Some people choose to use social media. There's probably a reason they're doing that."
Enunwa sparked the latest controversy Thursday night, firing off several tweets about being fined $27,900 by the team for missing two mandatory medical treatments. He called the fines "excessive," saying the situation could've been handled better.
Before that, guard Kelechi Osemele -- in a dispute with the team over a shoulder injury -- posted a letter from a third-opinion doctor who supported his claim that he needed surgery. Osemele filed an injury grievance and was released.
This has been a turbulent first season for Gase, who nevertheless received a strong vote of confidence this week from CEO Christopher Johnson. The Jets are 2-7 with a road game against the Washington Redskins (1-8) on Sunday.
Gase declined to elaborate on the Enunwa situation, saying it will be handled internally.
"We know how we do things," Gase said. "That's the way it is."
Gase, speaking before practice, said he hadn't seen Enunwa to discuss the matter, but a source said they talked Wednesday after Enunwa learned of the fine. Enunwa also spoke with Douglas in an attempt to discuss the fine.
Enunwa learned of the fine when he saw his name posted on a video board in a team room -- he wound up tweeting a photo of the video board. He was fuming and decided to go public because teammates were similarly outraged, a source said.
Posting fines for the entire team to see is an unusual practice, but Gase did it in his previous stop with the Miami Dolphins, a source said.
Jets union rep Kelvin Beachum said he contacted the NFL Players Association on behalf of Enunwa.
"We're already talking to the PA about it, so they'll put some things in place to see what's the course of action, honestly," Beachum said. "Conversations are being had."
In his tweets, Enunwa, who suffered a season-ending neck injury in Week 1, said he missed treatments Nov. 8 and Nov. 11 because of a home emergency and a Veterans Day lunch with his wife, a veteran. He acknowledged he should've notified the training staff, but he believes the fine -- the maximum amount under the collective bargaining agreement -- was "excessive."
"Given everything that's going on around the team, I thought this could've been handled so many different ways," Enuwa tweeted. "I've spent my time with the team trying to build myself up to be dependable and hardworking so this s--- hurts."