"Information that are not backed up with science grounds" かなりいい訳出ですが二つの小さなミスがあります.
1-"information" は複数形がない名詞です:
a book that is fun (単数) --> books that are fun (複数)
information that is interesting (単数) --> information that is interesting (複数) (そのままです)
"informations" はミスです、 単数形の"information"ははすでに "informations"と同じアイデアを表しています.
2- "science (科学) grounds" ではなく "scientific (科学的) grounds"です.
お勧めな訳出は:
Information that is not scientifically backed up.
(科学的裏付けの乏しい情報)
Information that lacks scientific proof.
Information that lacks scientific evidence.
(科学的証拠の乏しい情報)