Lens focus motor sounds louder after I briefly used it without mounting it properly — is it damaged?

If the lens still focuses and any stabilization feature still works normally, a louder sound by itself does not necessarily mean it was damaged. Briefly using a lens that wasn’t fully mounted is unlikely to cause internal damage that would make the noise steadily increase.

A few possibilities:

• You may simply be noticing normal motor noise more than before.
• If image stabilization is on, that motor can sound louder than autofocus.
• A poor mount could have allowed some dust in, which might contribute to noise, though that’s not certain.

Practical advice: keep using it for now if it performs normally, but pay attention to autofocus accuracy, unusual grinding sounds, or stabilization problems. If the lens is under warranty, it’s reasonable to have it checked. If not, many photographers would wait unless performance actually degrades or you have an important shoot and need to be safe.