Dissolvido, não. Banido, sim.
A duração do familiar é instantânea , por isso não há efeito mágico duradouro a ser dissipado. O familiar não é criado e sustentado pela magia, você apenas o altera para obter seu serviço.
The spell harms, heals, creates, or alters a creature or an object in a way that can't be dispelled, because its magic exists only for an instant.
(PHB 203)
O familiar é , no entanto, uma criatura e, portanto, pode ser afetado por mágicas ou habilidades que afetam as criaturas. Então, sim, poderia ser banido.
Banishment
You attempt to send one creature that you can see within range to another place of existence. The target must succeed on a Charisma saving throw or be banished.
If the target is native to the plane of existence you’re on, you banish the target to a harmless demiplane. While there, the target is incapacitated. The target remains there until the spell ends, at which point the target reappears in the space it left or in the nearest unoccupied space if that space is occupied.
If the target is native to a different plane of existence that the one you’re on, the target is banished with a faint popping noise, returning to its home plane. If the spell ends before 1 minute has passed, the target reappears in the space it left or in the nearest unoccupied space if that space is occupied. Otherwise, the target doesn’t return.
(PHP 217)