This is taken from the advert for Dolmio pasta sauce, featuring a happy Italian family who all end up with mucky red faces after eating spaghetti bolognese with too much gusto. The slang term describes the state of a man's face after performing oral sex on a woman during her "time of the month".
So he's gone to the bathroom for a slash, and discovers to his horror that he's wearing the Dolmio grin...
A dolmio grin is what happens when you go down on a girl when shes on her period and you get blood all around your mouth. It's called a dolmio grin because you get a similiar effect when you have lots of pasta topped with dolmio tomato paste.
Man I went down in this bitch and got the dolmio grin.