You can follow the below like on how to customize to show only required type of message. (public, private or task) from the below like at step 7 you can select required to message.

In the section, select the message types that users can post:

• To allow users to post public messages, select Message.
• To allow users to post private messages, select Private post.
• To allow users to create and assign tasks, select Task.

https://community.pega.com/sites/default/files/help_v82/procomhelpmain.htm#pulse/pulse-enabling-users-to-post-in-activity-feed-tsk.htm#Enabling_users_to_post_messages_in_the_activity_feed

***Edited by Moderator: Lochan to update platform capability tags***