Start by using a very gentle dishwashing detergent... Always start on the back of the tin (or any can) that way if the product you are using is too strong? The face of the can/tin will not be harmed...
Personally, I wet a tin completely, take a few drops of Dawn (that is the brand I use) place it on the tin and work it gently with my finger tips... I see how the drops of detergent are cleaning and go from there... If there is no damage to the tin, but things are not as clean as I would like? I have a very soft (child's) toothbrush that I add a couple more drops of detergent too along with more water... I gently, work the brush over a small area on the back to see if this is working to remove what I want gone?
Sometimes it does work, other times it doesn't... If it doesn't, I usually dry off the tin and say "it is good enough"....