Q. Can I limit iThenticate to only check a publication against a collection my own publications?
The Weizmann account includes the option of checking your work against a "private repository" (also known as "Your indexed documents").
iThenticate can check a single Weizmann repository -- not for specific authors. Of course, that repository will only contain publications if Weizmann authors choose to save their content in it.
Weizmann authors can save their papers to this private repository and make future comparisons both with this local collection and with iThenticate's database of publications separately.