I'm not sure but it must be هذه الحديقة غريبة. When you use a demonstrative adjective and say "this garden", that makes "garden" معرفة (definite) and therefore it takes the definite article and becomes الحديقة.
"haadha" when the noun is masculine, "haadhihi" when the noun is feminine. (Remember that all nouns in Arabic—objects, places, animals, concepts, etc., not just people—take one or other grammatical gender, and it's not always what you might expect.)