A "gauze square" refers to a small piece of fabric made of a thin and transparent material called gauze. It is often a square shape and is commonly used in medical settings to dress wounds or to help stop bleeding. Full definition
-- If you're having boys and they're being circumsized, have plenty of Vaseline in a tube (not the big jar — it's more sanitary) and small 2 ″ x2 ″ gauze squares handy (the hospital will provide some but once we were home we ran out in 2 days). (twiniversity.com)
For little circumcised boys you have to use Vaseline and gauze squares during the diaper change. (newbornbabyzone.com)
It was one thing to be the bloodied master of my own destiny, yanking my tooth out of its socket, triumphantly holding it in my fingers, going to the nurse's office and coming back with a small brown envelope and a bloody gauze square! (newbabynewpaltz.com)