Yes I think it will change the relationship between Steve and his mom. Ever since his mom left him Steve thought she never wanted him around and only cared about Beau. Shortly after she left with Beau she realized it was a mistake leaving Steve behind but by that time it was too late, he had already ran away. Because of that situation Steve always had the thought that she never did care about her. Now that he knows about the letter and she actually does care about him I think Steve will be able to forgive her. When Steve first found out about the letter he thought Beau and their mom was “studying” him but I think in the end he will realize they both just care about him.