I don't think it's relevant that OP frames the question around an interrogative construction. Grammatically, it's no different to:
[this] is to do with [that]
...which has tens of millions of (mostly relevant) instances in print. From Macmillan Dictionary:
have (something/anything) to do with
be something/anything/nothing to do with
to be connected with someone or something.
For most purposes, be and have are interchangeable here. Idiomatically, there are certain preferences. For example we very often include anything in interrogative forms based on be...
Is it anything to do with [that]? (11,200 written instances).
...and we often include what in forms based on have...
What has this to do with [that] (134,000 instances).
Note that be to do with is primarily a recent British usage. It's catching on in America, but current "prevalence" values are much lower. That much is certain; what follows is pure speculation...
Looking at early (pre-1970) instances of is nothing to do with in Google Books, you can hardly avoid noticing many are Kenya National Assembly Official Record (Hansard). In 1972 neighbouring Uganda expelled about 60,000 Indians/Pakistanis. Many of them were running successful businesses, and spoke relatively standard English; almost certainly they either influenced or were influenced by the dialectal variants used by politicians in the general region.
About half of the expelled Asians came to the UK. Overall, they were well-received and have thrived in their new home. My guess is mainstream British society adopted the new variant partly because of them, but here's the UK-based New Scientist - 22 Aug 1957...
If it is anything to do with I C I, of course, he will need no spurring.
...to show that it wasn't completely unknown even much earlier, in the ancestral seat of English.
Turning to the "grammaticality" question. The speed at which this variant has caught on means many Americans may rarely have encountered it until relatively recently, so they may find it "strange". But "grammar" really just means "what people say", so the sheer number of citations in recent decades is enough to say this form is already well-established. I've no doubt that in a few more decades it'll be as familiar to Americans as it is to Brits.