I don't know how true this is. My understanding is that tfl could set their own bylaws to a large degree .Absolutely not. TfL did request the Byelaws were changed but the Government denied their request; TfL have no right to fine anyone.
Internally tfl sent out a recommendation to the mayor that while it was ideal that people continued to wear facemasks on public transport requiring people to wear face masks would put staff at risk of assaults, stifle the recovery of demand and cause confusion where there was interfaces between tfl and other operators services. (Could tfl fine someone for getting off a GwR train at Ealing Broadway or a passenger getting off a national express coach at victoria?)
I believe that by having it in in conditions of carriage and not the bylaws this was a fudge between the mayor's wishes and tfls wishes TfL could also claim that facemasks were required when they were not.
There are also conditions in the bylaws. Where the highest penalty is ejection from the station ( such as having an unfolded bicycle on LU) I do not know if by merely having it in the conditions of carriage it would be grounds to deny travel in of it self. Every other aspect of the conditions of carriage have some element of legal backing in the bylaws.