Because reincarnation is when you enter a NewBorn Body for A Another Life. Basically a body that has just started its life. Meaning, you are reborn.
And they also did mention, she lived as Henry's daughter for 7 years PROPERLY before regaining her Past Life Memories. But even if she did have her memories back then, she'd still be considered a "Reincarnation". Unless the baby body was a few days/weeks/months old, it's not considered a Transmigration.
Transmigration is entering an already existing body/a body that is already living it's daily life.
She died in the past life and was reborn. After a suitable age for Brain Development, she recovered her Past Life Memories.

Why add the reincarnation when she still has the mindset of a child?