Moor Green are bottom of the Doctor Martins Premier League with just one point from six games, while Ilkeston are a place above them with two points.
Petty has played twice recently, but will see the move as an opportunity to get his form back, and also return to his native Midlands.
Youngster Burton meanwhile will be able to get first team experience under his belt. He has yet to make his debut for City after signing pro terms in the summer.
Meanwhile, Grimsby manager says that the decision to let striker Phil Jevons join City on loan was "purely for financial reasons."