The only complement this kind of "do" accepts is an active verb phrase (headed by a verb of action) with zero infinitival inflection. To the question "What can I do?", thus, you may answer "You can tell them the truth" or "What you can do is tell them the truth", or simply "Tell them the truth", BUT NOT "*To tell them the truth", which is a CLAUSE with a generic, invisible subject, NOT just a verb phrase. What complicates matters in cases like the one you ask about is that either a verb phrase or a clause can, depending on the subject, function as the attribute of "be" [identity-be: A is B = A is the same as B]. Hence, the sequences "is to tell them the truth" = [BE+ Clause] and "is tell them the truth" = [BE + VP] are both well-formed in themselves. Whether they eventually yield a grammatical sentence depends on the choice of an appropriate subject. You need a subject that can satisfy identity with respect to the clause or the verb phrase, respectively. In the example you mention the subject is a noun phrase ("The only thing to do" = “The only thing that one could do”) containing a reduced relative clause "[zero relative] to do _" whose invisible complement must be a verb phrase, as explained. Now, the antecedent of the relative (“the only thing”) must, by definition, also be a possible object of “do” (= an x such that to do x is the only possibility). That guarantees a legitimate identification between “the only thing to do” and what follows identity-be, i.e., “ask them to come half an hour later than the other guests” and the correctness of the sentence. Why can “to” (= the clause) appear as well, in this case? Well, because “thing” can ALSO refer to a complete event/state of affairs, cf. “There is one thing/something you do not know: I resigned this morning / I am married”. If instead of a noun phrase the subject is a free relative clause “What we can do”, there is no antecedent (no “thing”), and only something that can be the complement of “do” (and co-referential with “what”) can follow identity-be: “What we can do is ask them to come <….> guests” is correct, but “*What we can do is to ask them to come <…> guests” is not. In that case, there is no optionality: “to” is not possible.

In this case, it looks like the author wrote "was ask" instead of "was to ask" because there are already two "to"s in the sentence... One more would have been redundant... too many tos!

The sentence is alright without a TO.

The "TO" is optional.