I too almost always remove the condom myself, knot the end then if incall pop into a plastic bag. When touring I tend to use nappy bags, but I also collect bags from packaging, parcels etc, even bread bags (wash, turn inside out, dry). I then use wipes, place these in the same bag. After the end of the booking bag is knotted and binned (if touring I double bag then find a bin outside). Some outcall clients want me to take the condom away, often disability clients reliant on carers ask me to do this. Some of my outcall regulars who are environmentally conscious use one of their own clean towels, or go and wash rather than use wipes.
Incall will have laid out a clean hand towel for them in the bathroom, there's usually a clean bath towel in there too but if there isn't and they ask for or need a shower I have one to give.
By the way I am not 'tree-hugger', just makes sense to use the numerous plastic bags I accumulate from things I order online.
Taking charge of the condom means I won't find it discarded somewhere odd or inconvenient.