I have one of the June Taylor Square and Block boards, and also a small board I made out of plywood and covered. Both of them I have taken out back, hosed to get them wet and scrubbed with Dawn, sometimes bleach if really bad, and hosed to rinse. One spot only came out with lemon juice and sun. Just let the sun dry them. They are good as new. Trick is not to get them too wet, like soaking the board in the water.
I haven't tried to clean the ironing board cover. Mine has the painted grid on it. Has anyone tried to clean one like this? Afraid the printing will come off.