If it is about something belonging to Debbie, there IS an apostrophe. If you don't put an apostrophe it means that all Debbies glass people in pub brawls (attack them with a broken glass). I do hope that none of the Debbies I know are like that.
The apostrophe originally used to stand in for missed out letters in shortened versions of words run together - as in don't (do not) isn't (is not) it's (it is). A rule of thumb is to imagine it as "Debbie hers" shortened.
But strangely, where "its" is used in things like "My car is due for its MOT" there is NO apostrophe, probably because it's the whole possessive pronoun and not being shortened.