That not only looks bad, it is specifically addressed in the PGA Tour's handbook on player conduct.
Among the stipulations outlined in the gambling section, a player shall not "associate with or have dealings with persons whose activities, including gambling, might reflect adversely upon the integrity of the game of golf.''
At the very least, that suggests Finchem has to do something: a suspension, a fine, a scolding, a public rebuke. Something.
I'm guessing we'll get nothing for a few reasons.
One, they aren't going to break precedent with one of the game's biggest stars.
Two, the gambling association to me isn't enough, unless for some reason it was shown Phil was gambling on PGA Tour golf in a way that could be construed as shady. Also unlikely.
Three, Billy Walters was an AT&T National Pro-Am participant and champion. Phil can very easily say the PGA Tour introduced him to someone they would now be saying Mickelson shouldn't have been associating with.