What do invasive species do?
For example, weeds like crabgrass are seen as invasive because they aren't attractive / desirable for lawns. An example from antiquity would be fleas carrying the Yersinia pestis strain of the bubonic plague. Fleas traveled along the Silk Road and Indian Ocean Trade route from Asia into Europe where this wasn't common. Because the bubonic plague poses a significant risk to human health, it's considered an invasive species.
In short: they do damage.