My grandfather didn't __________________ phoning me last night.

The phrase "didn't have any recollection" is the correct choice because it fits the context of the sentence appropriately, suggesting that the grandfather does not have any memory of phoning the speaker. This choice emphasizes the lack of memory in a formal way, indicating that the grandfather may not even be aware that he made the call in the first place.

Using "have any recollection" also aligns well with the structure of the negative form of the verb "to have," which is often used to express a complete absence of memory regarding a specific event. In this context, the phrase effectively communicates that the grandfather is not only failing to recall but also has no awareness of having done the action at all.

Other choices would not convey the same precise meaning. For instance, "mention" implies that the grandfather would have needed to discuss or bring up the phone call, which doesn’t align with the intended lack of memory. Similarly, "recall" and "remember" suggest a more general failure to bring something to mind, but they don't capture the full nuance of total unawareness depicted by "have any recollection." Thus, "didn't have any recollection" serves as the most suitable and comprehensive match for the intended message in the sentence.