That is just an alternate usage/definition for remove that was commonly used in the US at the time. An example from The Lamplighter, the popular novel published in 1854 (the same year as the grave), 'Soon after the Sullivan's return from their excursion, the Grahams removed to the city.' Just means to move location.

Edit: Also born in 1808 in Pennsylvania, she could not have been born a slave (in Pennsylvania anyone born after 1780 was free).

Forgive me if this is against the rules, but where did you find this exactly OP? I'm in Tuscaloosa myself and it seems quite a fair sight older than most of the tombstones in the area. I'd almost say it was something from the Old Bryce cemetery, but the deceased passed before the hospital opened.

As a tangential question to the OP's, what would be a likely factor for someone to relocated from somewhere like Philadelphia to Tuscaloosa at that time period?