Can you prove that phrase "it's important that you to remove" is grammatically incorrect?
I found several times in books the structure with that-clause, where they put the infinitive with the particle "to" after "that".
For example, from Advanced Apple Debugging & Reverse Engineering by Derek Selandar (emphasis mine):
Since this book involves debugging not only your own applications, but any application you’re curious about, it’s important that you to remove this feature while you learn about debugging so you can inspect any application of your choosing.
I think it's incorrect. How can I prove it?
If you are asking how to prove it's incorrect I think by referring to the present subjunctive mood.
The word "remove" here is not an infinitive. It is in the subjunctive mood, which in this case looks like the basic form of the verb. However, if you changed the person into the 3rd one, the form of the verb wouldn't change: it is important that he remove.
It is a typical form if it is preceded by a clause expressing obligation, necessity.
It is formal, probably more common in AmE.
The subordinate clauses can take other - regular - forms but not a full infinitive. So also possible are:
It is important that he should remove... and
It is important that he removes...
https://grammar.collinsdictionary.com/easy-learning/the-subjunctive