I create round trips in OSRM and export the GPX file to load / use it in OSMAnd for a bike ride. After this I like to apply corrections but I cannot find the opposite GPX import in OSRM. Do I oversee something? Cam someone help me to solve the task? Thanks in advance.
You can’t directly import a GPX file into a routing engine such as OSRM.
OSRM routes are effectively made up of the routing engine’s chosen route between the “via points” you supply.
If you were to upload a GPX, the routing engine would have to calculate what via points were required to follow the route you took. This is a Hard Problem and not something OSRM will do out of the box.
Some OSRM-based routeplanners may have additional code to do that - mine does (https://cycle.travel/map) but it won’t get you a 100% accurate correspondence to every route you take (in particular, if you ride on a rough track or busy road that the routeplanner wouldn’t take of its own volition).
Thanks Richard. I asked for OSRM because it was my first choice compatible to german map style and metric dimensions, but I’m not tight to this router. I tried your proposed router which has no import for GPX, but I can live with the Save function (list of saved routes). Disadvantage: My existing GPX files I have to redraw / reroute to import it 
Do you know how to expand the list of routers in OSM? Maybe your router can be a list element to chose?