With or without tea

[Coffee Break]

I encountered the expression "With or without tea", but am struggling to understand it. Could you please let me know what it means? Here is the excerpt:

[The Protagonist] : “Do you enjoy making me sound stupid? Maybe I am stupid.”
[Clara] : “Maybe I am stupid,” she mimicked. “Two home runs in a row, Printz. Now it’s my turn—and I don’t know if you’re going to like it.”
[The Protagonist] : “With or without tea,” I interrupted, reaching for humor, however lamely.
[Clara] : “Teatime is long past. Here is what I have to say, and live with it as you please.”
[The Protagonist] : “Shoot.” A touch of fading irony in my voice, but I was buckling up for the worst.

- André Aciman, Eight White Nights, Sixth Night

This is a novel published in the United States of America in 2010. It is narrated by a nameless male protagonist. He meets Clara at a Christmas party in Manhattan. Now the protagonist is arguing with Clara, while attempting a humorous remark.

I wonder what the underlined expression means.
I am guessing that "with or without tea" might be attached to the previous sentence "I don't know if you're going to like it", though I am not sure.
And I am also curious how a suggestion for teatime can be "humor".

 

[dunchee]

I am guessing that "with or without tea" might be attached to the previous sentence "I don't know if you're going to like it"

You guessed correctly. The Protagonist tried to be funny by suggesting drinking tea at an inappropriate time. He/She, however, did say it was a lame attempt, so it's fine if you don't find it humorous.

 

[Ostap]

I think the joke was in assuming Clara's "it" (in "going to like it") was a reference to food/meal.

 

[Coffee Break]

@dunchee and @Ostap,

Thank you very much for the explanations.
Oh, so "with or without tea" is connected to "it" in the previous sentence.
The protagonist is suggesting teatime at the wrong timing, and he is also implying that she said "it" to mean some food, and as if he was suggesting some accompaniment to her "it".

So the protagonist is saying: "Now that you are coming with "it", I wonder it would be better if tea is accompanied, or not accompanied".

I sincerely appreciate your help.

 

[Tarheel]

@Coffee Break At the wrong time, not at the wrong timing.