Both of my kids knew many transfer students (some from their high school) at Cornell, and they all integrated well. By graduation time no one really remembered who were transfers. They offer GT transfers because they believe those students could be valuable members of Cornell if they had more space now.
My younger one got in through ED, but my older one fought hard to get off the WL. Initially she felt a bit less because she got admitted through WL, but she said she had the best 4 years of her life at Cornell. She graduated with high GPA and got her dream job upon graduation.
Try to make an unemotional decision about whether to take the GT transfer. If you are happy with your choice now then go with it, but don’t turn down the GT transfer just because you weren’t their “top choice.” Another way to look at is what is the harm in accepting the offer. It is a “free option” to you now. You can decide what to do with it later.