Chess Puzzle of the Week (404)

I’ve been looking through some of the games played at last week’s British Championships.

This position is from the Round 2 game between Koichi Nicholas and Trisha Kanyamarala.

The game concluded 37. Rh7 Qxc3 38. Rh8 Rxb2+ 39. Bxb2 Qe1+ with a perpetual check.

Could either player have improved on this?