Problem definition
In certain situations, a module can become permanently in a pending ingress state.
Usually, the cause for this is that a requirement for the module is not fulfilled.
Link to Module requirements here.
What is seen in the module registry for the module is:
If a user clicks on the module they get a constantly loading screen.
Solution
To delete the module click on the pending button itself.
Then you will be redirected to this page in your organization
https://app.terraform.io/app/<Organization_Name>/registry/modules/private/<Namespace>/mod-name/<provider>/status
Where you can delete the module from the Private module registry.