Of American-English origin, the colloquial, sarcastic phrase what has that got to do with the price of tea in China? is a rhetorical question calling attention to a non-sequitur or irrelevant statement or suggestion made by another person.

So well-known is this phrase that Ken Thomas only alluded to it in Fees set for Waupun poultry permits, published in the Daily Citizen (Beaver Dam, Wisconsin, USA) of Thursday 11^th July 2019:

Waupun—What did Tuesday’s Common Council meeting have to do with the price of eggs in Waupun?
Well, unlike the price of tea in China, the cost of a permit could have a big impact on the feasibility of keeping chickens for the relatively small number of residents interested in doing so.

The question what has that got to do with the price of tea in China? perhaps alludes to the phrase not for all the tea in China, which is first recorded in the late 19^th century and means not in any circumstances.

This is just one of the numerous questions built on the pattern what has that got to do with the price of ——?. In the questions built on this pattern, which dates back to the first half of the 19^th century, the noun following the price of is irrelevant to the context in which it is used.

However, the question what has that got to do with the price of tea in China? has occasionally been used literally, in relation to the actual price of tea in China. The following, for example, is from Hardy’s Wonderful Discovery, by ‘The Old Stone Cutter’, published in The Kansas Democrat (Hiawatha, Kansas, USA) of Thursday 5^th September 1895:

In answer to my question, how many more pounds of tea at 6 cents a pound can be bought in China for a United States gold certificate for $50,000 than for a United States silver certificate for the same amount, when bar silver is worth 67 cents an ounce. Here is his most wondrous reply: “As the balance of trade is 4 or 5 to 1 against us in our trade with China, the larger part of silver would, if we bought our tea with silver, have to be sent to some other country where the balance of trade is in our favor and the discount on silver would be the cost of sending it there, but if he bought his tea or any thing else in London, the silver or any other United States money would be worth the same as gold less the difference of sending it, just the same as it is now.”
Well, well! Can it be possible that these are the words of our ex-state representative, who has volunteered to instruct us on the silver question, or am I dreaming?
Will the learned gentleman kindly tell us what our balance of trade has to do with the price of tea in China or the parity of gold and silver in that country, or any other country in all the world.

The earliest occurrence that I have found of what has that got to do with the price of tea in China?—used as a sarcastic phrase—is from the column Nothing’s Bar’d from the Mill of R. Klare Bard, published in the Altoona Tribune (Altoona, Pennsylvania, USA) of Wednesday 30^th April 1930:

Ray ‘N’ Don have a couple of questions to ask. If I slip up, you can take your best hold and call the mistakes to my attention.
The first question is: “Does a steeplechase rider rate a trophy when he makes a dive into the water as his horse leaps a hedge or hurdle?”
Answer: The trophy would probably be a cup for the fancy diving championship.
The second question: “If the big rubber men keep stretching things, how many mucilage men will it take to make the Union stick together?”
Answer: On third Fridays in July. But what has that to do with the price of tea in China?

More generally, the phrase the price of tea in China was used jocularly in the early 1930s. The next earliest occurrences of this phrase that I have found are as follows, in chronological order:

1-: From the column Nothing’s Bar’d from the Mill of R. Klare Bard, published in the Altoona Tribune (Altoona, Pennsylvania, USA) of Saturday 9^th August 1930:

Mike McNally has the low-down on the world series… “Watch McGraw” sezze… Let ’em win… Let anybody win… And the price of tea in China will not be affected thereby… Charlie Schwab is coming to the city… What’s Bethlehem going to do, Charlie? [&c.]

2-: From an interview of the U.S. film actress Esther Ralston (1902-1994), by Jack Proctor, published in the Los Angeles Record (Los Angeles, California, USA) of Saturday 21^st March 1931:

It was only in the last few minutes before I left the Ralston home that we got around to discussing motion pictures, for the actress—believe it or not—is about as much interested in the film business at present as she is in the price of tea in China.

3-: From the column The Sportscope, by Joe M. Butler, published in The Scranton Times (Scranton, Pennsylvania, USA) of Friday 14^th August 1931; the following is about a baseball player called Pat Wright—whether this baseball player was really a stock-market expert discussing the price of tea in China during intermissions cannot be inferred from the context, but I am inclined to think that, here, the phrase is used jocularly:

Between games he enjoyed a bottle of pop, a hot dog, discussed the price of tea in China and the high and low on the stock market for the day. Then he resumed where he left off in the initial struggle. Bam! Another blow and the leather sailed yards over the right field fence.

4-: From Little Enid, the Daily True Story by Lewis Allen Browne (1876-1937), published in the Evening Courier (Camden, New Jersey, USA) of Friday 9^th September 1932:

The Saturday night dinner wasn’t quite as cheerful as usual.
[…]
There was an awkward silence and […] Mr. Spurlow hesitated and turned solemnly to his son-in-law.
“What,” he asked, “do you think of the price of tea in China and the morals of the Fiji Island girls?”
And when Tom Harlan laughed uproariously at this, Clarissa left the table hastily, followed by her mother who sought to comfort her.