Spray with neem. Insects that are small are hard to know if gray is the adult, or the other way around. A twofold approach is to use neem as a spray on all the foliage and a Bt form for a soil drench. Fungus gnats are tiny and black color. There is also a whitefly. Whiteflies can get trapped by yellow sticky pads placed near the plants horizontally. The yelly sticky traps can also catch fungus gnats. The sticky material is waterproof, but also attracts dust and debris that blows around, so they should be replaced when covered with bugs.

IF these little critters look JUST like teensy grasshoppers, then it is quite likely that they are grasshopper nymphs. Grasshoppers are extremely small when they hatch from their eggs. They are able to hop all over the place, but cannot fly until they grow up. They shed their skin periodically, and will change their color (and size) as they do so. SO! Take a good look and let us know if you're sure that they are grasshopper babies, or not.

Another clue is that the nymphs of grasshoppers feed in just the same way as the adults. They eat foliage. If you have a lot of them, then your basil plants will end up, piece by piece, into the tummies of these little guys, who won't stay little for very long.

At this early stage, insecticidal soap would be helpful, as would neem oil.

Here is a site that features many organic based products for insect and disease control. Neem is quite mild and is not harmful to other insects, unless its sprayed directly on them. It should be applied every 10 days or sooner if it rains. The vegitation can be eaten even after spraying, so a simple wash is just fine. There is a company that sells it by the gallon, undiluted and also offfer Castile soap as the sitcker spreader for it. Gardens Alive has it as well and its mixed with some kind of aromatic solvent, like alcohol or something. Its clear, but turns cloudy white when mixed with water.

Here is a link that might be useful: Organic supplies