Well, that's rude... :S
Do you have to have the 'o', or can you just say "Ela recusa meu presente?"
The definite article is optional for possessive adjectives (used before a noun like my), but is required for possessive pronouns (used without a noun like mine).
More info here
I was totally offended on behalf of the gift-giver... :P
Acho que se emprega Ela rejeita o meu presente