Wipe up unused water in a paper tissue and put the tissue in ordinary waste.
Be careful to avoid staining, see How to use.
Dissolve an unused applicator tip or pencil point in salt water (half a teaspoon of salt in an egg cup of water is sufficient). The resulting wet residue can be placed in ordinary waste or flushed down a sink.
The bare plastic applicator and empty pencil holder can be recycled with other plastic waste.