Spider mites may also do damage that looks like that. At the left side of your second picture I was thinking there may be some tiny webs. Take a look with a magnifying glass.
If that's what you find, is there any way you can take the tree outside and hose it off? If you can do that a few times in the next week or two, that will break the life cycle of the spider mites without using a whole lot of chemical stuff. If you can't do that, the next non-toxic method is a soapy water spray, 1/2 tsp. dish soap to a quart spray bottle and spray the whole thing, tops and bottoms of leaves, stems, soil surface and all. You'll have to repeat the soap treatment within a week as well, to get the next generation that may be still unhatched. Three treatments is best.
But I like the hose method above all, and the plant will love being washed, too.