Sounds like the best explanation to me. Tetras will scatter their eggs so it isn’t too difficult for them to wind up on the filter.I cant remeber exactly. But im pretty sure the sponge on the sponge filter i took from the main tank. I always leave a sponge on the filter intake of my main tank. So most likely i filled up the hospital tank and then got the sponge from my main tank to use in the hpspital tank. So probably thats how the eggs got into the tank?