If any education information is entered/updated through a profile update or new user signup in NetCommunity, The School Name field will be required
This is because The Raiser's Edge requires the school name for any changes/updates related to education, therefore, it cannot be deselected in the plugin.

Reference Article: Unable to remove School Name on a Profile Form or New User Registration of the User Login

Although you cannot deselect the school name for inclusion on the record, you can change what was entered by the user by clicking on the school name field in the "New Value" column.

This will allow you to select a more desired value from a dropdown list of School Names entered in The Raiser's Edge.