Thanks for the vote of confidence CrystalMoon but my knowledge is very limited in the rather extensive area of “medicinal uses” of plants.
The first question I would ask is what sort of mite? There are thousands of types but only a very few feed on reptiles and only the Reptile or Snake Mite Ophionyssus natricis is considered a serious problem due to its ability to spread diseases. This is an obligate reptile parasite (only feeds on reptiles) and as such can be eliminated from a collection. The only mode of transmission is bringing in an infested animal and placing it in near contact with clean animals, or carrying mites from an infested animal on clothing or equipment that is then brought in near contact with uninfested animals. As far as I am aware, it is not yet known to occur in the wild in Australia, so contact with wild reptiles through outside cages is not considered a problem. Therefore, minimum quarantine procedures for new additions, and after contact with other reptiles, are all that is required to maintain your collection free of this particular pest.
There are several species of bright red or orange coloured mite that occur on geckos, skinks and dragons. They do not appear to do much damage and do not seem to survive well in the drier conditions of captive enclosures. Covering them with Olive Oil using a cotton bud will suffocate them. They then fall off when dead – in a day or so.
Pyrethrum daisy is the most commonly used insect repellent (and for other arthropod pests). Most of the mints are also said to keep many insects at bay, such as ants. I personally think you are better off to rid your collection of any mite and plant things that look good or are edible, like some of the dwarf lomandras, strawberries, cherry tomatoes (in season), Warrigal greens (native spinach), Dianella (attractive with edible berries), ruby salt bush (edible berries) and even dandelion weeds.
Just so you know: My plant knowledge centres around species recognition and growth of smaller garden plants, making my own potting mixes for succulents, orchids, bromeliads, “indoor” house plants etc and identifying and growing native plants from seeds and cuttings. The latter alone consumed many years of my free time and we were very successful at it.
Blue