We're not aware of what restrictions the building management might be referring to (except, of course, any pesticides not labeled for indoor use). These do appear to be Multicolored Asian Lady Beetles, though it's difficult to be positive from the photos, as several ladybug species occur in Maryland. However, MALB do tend to be the one overwintering indoors most of the time.

A pesticide treatment is not necessary, and would likely not work well anyway because the insects would have to come into direct contact with spray residues, and it's not practical to treat the entire ceiling, window sills, walls, light fixtures, etc. that they may be wandering across. Such sprays are also indiscriminate, so harmless insects that might wander around if trapped indoors by accident would also potentially be killed. There is also no bait station that we are aware of for this ladybug species that would attract and trap them, at least not in spring when they are not trying to aggregate.

They enter buildings in autumn seeking shelter for the winter, so the simplest long-term solution is to have building maintenance try to better-seal any exterior wall gaps and cracks, vent covers, window or door weather-stripping, etc. Blocking access is the best way to keep these and other nuisance insects out of buildings. Once inside and resuming activity now that the days are lengthening and warming, which "wakes" them up again, they seek sources of light trying to escape the dark environment they find themselves in. Insects generally associate a light source with open sky. This is why they'll gather around windows or light fixtures; they are trying to get back outside.

As they run out of stored body fat to subsist on and dry out because there are no sources of water to drink and no insect prey as food, the ladybugs will die out. If sunny windows can be opened, that might at least give them a light source to travel to where they can be caught and tossed outside instead of wandering into light fixtures.

Miri

You're welcome!