I'm thinking he doesn't.
He's terrifyingly outclassed by major league hitters. While I'm no huge fan of tossing a lot of starts at Elizardo Ramirez or Tom Shearn or Kirk Saarloos, they're at least viable disaster options. You can start them and have some hope you can get out of the game without surrendering double digits and without demolishing your bullpen along the way too.
Dumatrait needs to go away, at least for the rest of the season.