Stainless steel travel mugs can be washed by hand in warm water with gentle soap. Scrub the inside and carefully wash and rinse the lid. Some mugs are dishwasher safe, but while this is convenient, some users worry about long-term damage to the insulation or dents and scuffs to the exterior. Some dish detergents and dishwashers may also leave behind a residue or odor, which can affect the taste of your beverage.For convenience, use a slender bottle brush to clean the inside of your travel mug. These have bristles on the end of a long, thin wand that can get into the hard-to-reach corners and edges at the bottom of the mug. The small bristles are also ideal for cleaning the lid.