There is currently no way to hide posts from a certain group of users. However, if you are the owner of the padlet, you can turn on post moderation. If you do, every time someone tries to post on your padlet, you get to decide whether that post appears on your padlet.
Here's how to turn on the require approval feature for your padlet.
How to turn on require approval
Post moderation can be enabled in order to hide unapproved posts. These posts do not display until the padlet owner approves them.
To enable this feature, open the Settings panel by clicking on the Settings cog icon (⚙️) on the right side of your padlet. Next, go to the Content section. Click the dropdown menu next to Moderation and choose from 3 different options: None, Auto or Manual. For this particular use case - you will want to choose Manual. This requires all posts to be approved before it is shown on the padlet.
Settings cog icon (⚙️) > Content > Moderation > Manual
When someone writes a post, it will not appear to others until the creator or an admin of the padlet approve that post.
For example, this is what a padlet would look like to the user who posted the content but it had not been approved by the owner or admin yet:
This is what the padlet would look like to others since the new posts aren't approved:
And this is what you as the owner of the page would see:
Once you approve the posts, everyone will be able to see them.