I think Baja gives you the best advice, but if you are willing to invest in some expensive but effective miticides there is probably a way to keep the pup. I have not had many cases of Aloe mite and mostly just thrown affected plants away, but on a different plant website I am a member of there are a number of serious aloe growers who have had success using miticides that we came to learn about because of Agave mite, on Aloe mites.
The most affordable of those is AVID (you can definitely get it on amazon in the US, not sure about Canada). Other miticides are Forbid and Pylon (with the latter you need to make sure you get something that you can spray and is not a one use fogger can that requires an enclosed space and is one use only).
Regular products that are active against spider mites will not do the job, Aloe and Agave mites, different species of the same bug family, are microscopic (I am sure Baja has info in his write up) and live inside the plant.
The protocol would be to isolate the plant and spray it several times in a 2-3 month period and observing new growth.
Another note: Aloe mite will not move into Agaves, and vice versa they are pretty plant family specific.
As to stress bringing them on, I would tend to agree with Baja plant stress does not make the plant get them, but I do think stress can lower the natural defenses that a plant has to the point that an existing Aloe mite population can manifest itself outwardly. This has been observed especially in Agaves, where stressed plants are much more likely to get a bad infestation whereas healthy happy plants appear to have a better chance of overcoming and growing through the infestation. The plant probably came with them, unless you live somewhere where neighbors are also avid Aloe growers as they can be windblown. One thing to remember is that bringing a plant home from a nursery (or getting it shipped to you) is a stressful event as growing conditions tend to change and in the nursery care of the plants may be very different than the care you provide, which can also be a stressor.
In Arizona you can now find Agave mite in wild populations that are extremely remote, so it may be something that has been a feature of Agaves for a long time, but now that we have been in a protracted drought populations are under enough stress that the mites manifest...
If you are worried about introducing these into your collection you will always want inspect new plants carefully, but that is probably not enough as they can be in the plant and not be observable, so people who worry a lot, keep new arrivals isolated for a month or two as they observe new growth and the really serious collectors spray preventatively with one or more of the aforementioned miticides.
