D&D 5E Quick Unarmed Strike question

[Charlaquin]

Yeah, to be clear, we agree: the RAW does not allow an additional unarmed strike as part of TWF. Someone upstream was wondering why that's the case, which I think is a fair question given how low key that additional 1 point of damage is and how much sense the idea makes set next to other parts of the rules. The buff to grapple builds based on allowing that extra grapple attempt keyed off the BA unarmed strike was the best reason I could think if that it wasn't allowed.

What Ovinomancer is saying is that, even if you allow an Unarmed Strike as a TWF bonus action attack, this would not allow an additional grapple. A grapple is not a kind of unarmed strike, it’s a special attack you can make using the Attack action.