Owlbears don't have the capacity to reason to come to that desired outcome. They attack what they see, don't know the concept required for them to come to that outcome, the ability to stop them attacking is all you should get. Feel free to look up terms such as unaligned and owlbear through 5e to understand why what you wish is not available.
Letting someone who means you no harm heal you is no moral decision. And the INT score should make basic reasoning possible. So my take from the Moms side would be: Here is a friend (animal friendship) that can lessen my pain and makes recovery faster. Even if it sees the injury as not so bad. And a healed up Mom can better
protect its cub. In addition to that 2 eyes are better than one
