"Pecking of" or "Pecking on"
Solution 1:
First of all, do you mean it’s or its? Seems that you are referring to pecking being done by the owl so the possessive pronoun “its” is what you want, no?
In regard to the pecking, it should be either “pecking on” or “pecking at” in this context. If necessary you could even say, “... pecking sweet fruit.”