Bonjour T,

If you had Le Passé du Subjonctif (j'aie pu), it would imply that your ability to bring the dish back was over, which would sound very strange here as the action of washing up (lave) is in Le Présent du Subjonctif. 

Le Présent du Subjonctif (je puisse) is the correct tense as it implies that 1. you're doing it now and 2. the action of being able to bring the dish back is still ongoing.

I hope this is helpful.

Bonne journée !