What is ironic about Sir Gawain's

acceptance of the sash from the lady of the castle?

Sir Gawain's acceptance of the sash from the lady of the castle:

Sir Gawain had accepted the challenge of the Green Knight who was to return Gawain the blow after a year and a day at the green chapel. The Green Knight was in reality Lord Bentilak who is part of a game devised by King Arthur's Sister. He is also Lady Bentilak's husband.

In the end, we come to know that the Lady was also a part of the game to test Gawain. The irony is that those who give the challenge and threaten to kill Gawain give him a sash to protect him.

He accepts the sash of protection from a lady who is a part of the game plan to test him. Irony means a situation contrary to what is expected.