In your Slack workspace, go to "Settings & administration" > "Workspace settings" > "Permissions."
Check, you will see settings related to the Slack for HubSpot app or there are options to control access or visibility within channels or do complete configurations related to actions, notes, and tasks. Look for options to limit access.
and then check HubSpot's user permissions settings to ensure that only authorized users have access to create notes and tasks.
Limiting the Slack activities to certain users in the workspace/channel
SOLVE
I'm not sure if the native hubspot slack integration supports this feature. Might be worthwhile checking out an alternative solution we built-- trysidekick.com which can be used to integration slack and hubspot. With Sidekick, you would be able to update record properties, create tasks/notes etc and also restrict it to certain users who can perform these actions using the user mapping option.
In your Slack workspace, go to "Settings & administration" > "Workspace settings" > "Permissions."
Check, you will see settings related to the Slack for HubSpot app or there are options to control access or visibility within channels or do complete configurations related to actions, notes, and tasks. Look for options to limit access.
and then check HubSpot's user permissions settings to ensure that only authorized users have access to create notes and tasks.