How to politely point out a basic mistake in a published top tier journal when working on some extension of the paper
That depends on the consequences of the mistake. Does it invalidate the main conclusions of the article or is it only a side issue? If the former, you can write up what the consequences are and present the new results as an article an submit it. If it is only a side issue, you can mention it in a footnote when writing up your results for the open problem.

In the former case, keep the tone professional: don't use any adjectives to describe the mistake and certainly not when refering to the authors, i.e. it is a mistake not a basic mistake. Focus on the point you want to make, and let the strength of the argument speak for itself.