Dealing with late assignments as a teacher assistant
Follow your stated policy, and follow it to the letter.

An important aspect of teaching, particularly with regards to assessment policies is that you have to be consistent in how you assign your grades. A main reason for this is that if questioned, you can draw upon the stated policy (especially if this was made clear to the students prior to the assessment).

In the case you described, as @ff524 stated in the comment, grade the mandatory part as normal, and apply the lateness penalty to the optional part of the assessment.

Essentially:

Mandatory part mark + (Optional part mark - lateness penalty applied to the optional part only) = Overall mark

(Note in the equation above, the equation in the parentheses has a minimum value of zero)