Go to your local auto parts store and by a cheap can of brake parts cleaner. It is a combination of petroleum solvents and should work excellent. It also evaporates really fast and leaves virtually no residue.
Or, if it is pure grease you are trying to remove, the brake parts cleaner will work great, but a can of degreaser will work even better, again it is just a mix of petroleum solvents.
These come in spary-paint size cans, and if you live near any city larger then ~3,000 people they should cost less then $2 American, and likely to find them on sale for less then $1 American.
They are excellent to have around, great for cleaning off the bar-b-q and anything troublesome on metal.
The other advantage of these is that they are in a compressed form, and so when you hook up the cheap nozzle (the long red thing) you can get precise aim with a decent bit of pressure it hard to reach locations.