@Antanicus I don't think you can. Both #OSMAnd and #MapsMe are showing vector based maps. So it's really a question of styling and software programming. They don't use 'tiles'.
If you like Maps.me over OSMAnd (I do too). why not switch to MapsMe? Why bother with OSMAnd? There's a FLOSS fork of MapsMe called "Maps" on fdroid which doesn't include adverts or tracking.