It's not that difficult ;-) Rinse by hand under water and add a little washing-up liquid. Nothing with a dishwasher (aluminium parts don't like it so much...)

After use, just rinse with hot water - possibly with a little washing-up liquid.
Still looks like new.

I occasionally put the inserts in the dishwasher, otherwise I wash them (and the rest) by hand.

Rinse by hand