Offered
In one account, the towel crosses the space between two players at a tense change of ends. The offer is accepted. When the moment is retold as the beginning of a reconciliation, this is the gesture people remember: something ordinary passing from one hand to another.
The cloth is easier to picture than the words that followed. In the telling, it comes to carry much of their weight.
Taken
Another version begins with the wrong towel. One player reaches for what they think is theirs. The other sees a hand taking something that was never offered. Here the exchange starts the argument.
From a distance the movement might look much the same. Up close, ownership, intention and permission change the whole scene.
Between the accounts
Some customs give acceptance of the towel the power to mend the pair. Others insist that everything depends on whether it was offered. The Lovers, Temperance and the Shared Court gather around the small negotiation: what is given, what is welcome, what still needs to be said.
The inventory keeps both versions. An offered towel can be declined. A mistaken one can be returned. Folded back on the bench, it looks much as it did before either player reached for it.