I don't think she gave up the baby, but arranged for someone to keep her until she could find a closer person she could trust to be the caregiver for her little daughter. The groundskeeper's wife doesn't even know Edith is the bio mom.
She did say there was no formal agreement between her and the Shroeders in Switzerland, and there isn't any formal agreemen between her and Mr Drewe either.
Just a small point, but Drewe is a tennant farmer, not the groundskeeper.
What do you think?