Is saying “Back to home” incorrect?
Yes and no.
“Back to home” would be correct if home was used as proper noun, a specific name for a place, and would thus need to be capitalized; “Back to Home.”
Inserting an adjective would make it work as well; “Back to my/her/his/their/etc home” or “Back to the white home.”
Inserting a noun, such that “home” becomes the adjective; “Back to home base,” “Back to home page.”
Finally, omitting “to” will make it correct as well; “Back home.”