There's certainly multiple factors to consider.
Despite what GA said about playing him, I get the feeling TW might have been on the bench more often than not if he stayed. In which case, it was tying up a wage.
Also, if GA didn't think he had adequate cover in the striking department, it may have been a different story regarding his release.
GA also mentioned they had been aware of the possible situation since the summer and always have counter-signings planned.
If there is another signing planned, even if it's not a direct replacement, getting money now might help move things along.
Finally, GA and the club might be of a similar opinion to some on here that TW won't be as a big a goal threat at Utd as he was here.
It would have been good if TW had waited until the summer to announce his move, but while I'd have liked him to stay, I'm less concerned about losing him that I was about losing Louis Moult, as I feel we are better placed to cope without him. Time will tell.