There isn't a way out now.
If they bring him back Dorries, John Hayes etc will whine.
If they sack him ITV will swoop and probably pick up a few other defectors.
Lineker is an extremely skilled presenter. I'm not pretending he's irreplaceable just very good and it won't be easy to slot in a replacement - particularly if there is an alternative programme available featuring the usual team.
And in amongst it all they've revealed quite how terrified the BBC really is of the Government and their impartiality shield (such as it was) is shredded in the process.