The lawyers for the patent holder pressed the federal judge to impose

As vivesomnium noted above, "they" is a problem in both A, C, and D-- the only plural antecedent in the sentence is "lawyers." Clearly ,the intended meaning of the sentence is *not* that lawyers should act or be saved from economic damages. Or you could say that there is potential to group the lawyers and judge together into a plural unit, rendering the pronoun ambiguous. In either case, knock those choices out.

B (and D) contain another issue, though. See that front-end split among the answer choices? "They should" and "the judge act" both appear twice.

That word, "should," might have triggered a red-flag in your head-- we're in the realm of SUBJUNCTIVES!

Remember there are certain words (we call them "bossy verbs") that require the subjunctive mood. Verbs that indicate desire, suggestions, orders, etc. fall into that "bossy verb" category and require the command subjunctive. To construct the command subjunctive, take the infinitive form and cross off the "to."

He demanded that she [strike]to[/strike] STOP the car.
She required that he [strike]to[/strike] START the class on time.
Carl should [strike]to[/strike] BE the best man at your wedding.

B and D incorrectly attempt to apply the command subjunctive! The verb (or verbal, here, since "arguing" has a modifier function not a working-verb function) is NOT a "bossy" verb. Arguing isn't pleasant, but it's a back-and-forth process, not a one-way request or order.

That only leaves E, which CORRECTLY uses the subjunctive "should BE" and unambiguously uses the pronoun "their" to refer back to "lawyers."

Hope this helps.