Building on what @atwhite shared, the `integration.UserProfileUpdated` webhook might be a good starting point here.
The API doesn't expose a native timestamp for when a profile was last updated. But the webhook payload gives you `userId`, `profileField`, `value`, and `oldValue` every time a profile field changes.
One possible approach: when the webhook fires, you could use the `PUT /user/{id}/profile_field/{field}/{value}` endpoint to write today's date into a custom profile field, effectively creating your own "last updated" timestamp. Since custom profile fields can be set to hidden, this could work without it being visible to the user.