The answer of the Teutonic Order, as opposed to the complaints of Poles – is very informative, specific, filled historical details. It referred not only to Vytautas and Jagiello, but Skirgaila and Kęstutis, and the baptism of Mindaugas. The answer in some detail illuminates the struggle of Vytautas for the throne Grand Duke and is a very good addition to the Lithuanian story, recorded in "Tale of Vytautas" (maybe even that used Vytautas memorial. But I have to leave this question open for further research).
Now we consider only mentions of the Tatars in this answer. This document addressed the theme three times.
In general, it must be admitted that the Tatars participated in the Battle of Grunwald made a strong impression on the Germans (and therefore, it was the right step by Jagiello and Vytautas). The Germans accused them of violating the solidarity of Christians (Catholics, of course), and attempts to harm the Catholic faith, represented by them, Germans.
This document does not contain mentions of the joint action against the Tatars in the campaign on Vorskla.
Full text of section – in the Ukrainian version.