I've read here on the forum about people putting a little piece of a BT 'dunk' down the filling tube, and using a fine mesh screen to cover the drain hole and filling tube. There's also videos on Youtube with people talking about how they're dealing with them.
Here it's so hot that the boxes need to be refilled twice a day and I think that washes most of the eggs out. I also hang a mosquito trap that attracts them with CO2 from yeast then, sadly, kills them with salt water. (It's from Spartan Mosquito out of Mississippi)