Teutonic Calvary do +2 damage vs faster units.

This would apply to Woad Raiders, cav archers, knight line w/ husbandry, camel line, light cav line, and nearly all of the mounted unique units. Genitours, Tarkans, and Cataphracts would need husbandry to be affected. Also, Teutons do not get light cav so this will only be useful for the knight line.

The most common idea to buff Teutons is to just give them husbandry. Here is the relevant AOE zone thread: https://www.aoezone.net/threads/husbandry-for-teutons.146569/

TLDR: Giving Teutons husbandry ruins their unique playstyle and identity. Their knights are already resistant to monk conversion, the strongest counter to knights. This would make Teuton knights too OP.

Additionally, giving Teutons Husbandry will make them their tech trees nearly identical with the Persians but with worse eco. There would be no reason to pick Teutons over Persians in a competitive setting.

https://ageofempires.fandom.com/wiki/Teutons/Tree

https://ageofempires.fandom.com/wiki/Persians_(Age_of_Empires_II)/Tree/Tree)

With this bonus, the Teutons wouldn't have to run away from faster Calvary and take unnecessary damage. It may also force your opponent to go for slower counters to knights like pikemen stalling the game out and giving the Teutons time to get to IMP where they can shine.