|Brogue The Rogue|
Are all the requirements met?
Furthermore, if you are on your home plane when you cast this spell, nonevil extraplanar creatures within the area are instantly banished back to their home planes. Creatures so banished cannot return for at least 24 hours. This effect takes place regardless of whether the creatures hear the blasphemy or not. The banishment effect allows a Will save (at a –4 penalty) to negate.
Creatures whose Hit Dice exceed your caster level are unaffected by blasphemy.
So is the caster on his home plane? Is the eidolon an extraplanar creature? Does it have fewer hitdice than the caster's caster level? And did it fail its will save? If so, then, yes. Bye bye, stupid overpowered critter.
If the eidolon mechanics calls out dismissal and banishment exclusively, than no, this would not work. If it is not an exclusive list, however, than it WOULD work.
The eidolon cannot be sent back to its home plane by means of dispel magic, but spells such as dismissal and banishment work normally.
Looks like it's not an exclusive list. Thus, looks like Blasphemy will work.