Normally I would recommend high pressure water, but you don't really have an option to do that.
Sysclean is meant to work well, but that's not free so you might not be interested
Vinegar is another thing that I've heard about using, dilute white vinegar in water and try that out.
The easiest way often is to simply use a q-tip to try and rub the residue off, works a lot of the time
What is "sysclean" ???