If you gave back a different form and the hospital doesn't bother to check it's their fault. Sending back amended contracts back to back during negotiations is completely normal.
There is a difference between informing them you are modifying it or sending back a clearly edited version and stealthily modifying it in the hopes that they won't notice.
I don't think it's going to hold up if you surreptitiously modify it in bad faith.
I don't think it's going to hold up if you surreptitiously modify it in bad faith.