That contributes to your culture, if not your genetics, so it is worth knowing to some degree, and if you have the information it can also be helpful to others.
This page is probably helpful: https://www.wikitree.com/wiki/Help:Non-Biological
You get to that setting when you click "Edit" on your great-grandparent's profile, and on the right it will show Mother and Father, with options for them. You can do this after entering his legal parents.
Unfortunately WikiTree doesn't have a way of tracking multiple sets of parents, so if you ever do find his biologic parents, you'll have to handle that with a note in the bio section.