Remember that a gerund (-ing form of a verb) can be a noun. Therefore, it can be possessed like a simple noun. At first, this is difficult to understand. Most people assume that the gerund is a verb, an action. But unless the gerund is preceded by a conjugated form of the verb “to be" it is not a verb. Often, it is much easier to understand if you replace the noun gerund with the expression: “the action of…" (That is, of course you can possess the simple noun, “action.")
They were quite pleased with our asking about the new TV.
(They were quite pleased with our “action of asking...")
My singing is very unpopular in my society.
(My “action of singing....")