My guess would be that it’s a conflation of two phrases:
From the OED, tea, n. (1989:
not for all the tea in China (colloq., orig. Austral.): not at any price.
1937 E. Partridge Dict. Slang 148/1 China!, not for all the tea in, certainly not!; on no account: Australian coll.: from the 1890’s.
1943 K. Tennant Ride on Stranger ii. 19 I’m not going to stand in my girl’s light for all the tea in China.
1958 J. Cannan And be Villain vi. 137 She wouldn’t get into a sidecar or on a pillion for all the tea in China.
1978 Radio Times 11 Mar. 25/5 I wouldn’t change Newcastle for all the tea in China… It’s a lovely place to live in.
And again, the OED, price, n. (March 2007):
what’s that got to do with the price of ——? and variants: what is the relevance or importance of that?
a1860 T. Parker Speeches, Addresses, & occas. Serm. (1867) II. 208 What has Pythagoras to do with the price of cotton?
1920 E. St. V. Millay Aria da Capo in R. Shay & P. Loving Fifty Contemp. One-act Plays 434 Can’t act! Can’t act! La, listen to the woman! What’s that to do with the price of furs?—You’re blonde, Are you not?
1928 Youth’s Companion 16/1 What’s that got to do with the price of eggs?
1949 N.Y. Times 1 Sept. 25/2 Someone has stolen the Blarney Stone and an American insurance investigator has been sent to find out who. (Obviously this doesn’t stand to reason, but what’s that got to do with the price of ale?)
1998 P. Grace Baby No-eyes (1999) xxxvii. 286 ‘You’ve got to get rid of me some time, you’re thirteen.’ ‘What’s that got to do with the price of fish?’
My guess would be that what’s that got to do with the price of tea in China is not all that old, from the latter half of the twentieth century. BYU’s Corpus of Contemporary American English has a cite from 1992, but I’m sure it’s older than that by some decades.
I found this in Linnaeus’s Elements of the Science of Botany, London, 1809, 56 (Google Books), although I’m sure it’s a random collocation of the words and has little to do with the modern phrase:
If the Europeans were entirely to cease from trading in it, it would very little affect the price of tea in China.
I’ve also found a number of instances of “price of tea in China” in British parliamentary debates from the nineteenth century, but again, unrelated to the phrase (unless we suddenly find antedatings going back over a century).