I heard of . . . . . . . . going to Agra.

A possessive pronoun shows ownership or possession. It replaces a possessive noun phrase (e.g., "the book of John" becomes "his book").

Let's examine the options:
Option A: theirs – "Theirs" is a possessive pronoun indicating plural possession. It would be correct if the sentence were something like, "I heard about the trip; it's theirs." This sentence doesn't show possession; it describes the people going. Therefore, it's incorrect here.
Option B: they – "They" is a third-person plural pronoun, referring to a group of people. It's a subjective pronoun (used as the subject of a verb) and this sentence requires a possessive adjective.
Option C: their – "Their" is a possessive adjective. It shows that the people going to Agra possess the action of "going." This correctly modifies the gerund "going," which functions as a noun.
Option D: them – "Them" is an objective pronoun (used as the object of a verb or preposition). This sentence does not require an object pronoun; it needs a possessive adjective to modify "going."
Therefore, only "their" correctly fills the blank, making the complete sentence "I heard of their going to Agra."