In a Grid Edit Report, make a field mandatory if another field is checked

Form rules do not work on grid edit reports. However, if you request Quick Base for the early release feature called "Data Validation" you may be able to validate that if the delete checkbox was selected and the reason is blank, you can throw an error message and prevent the data from being saved.

Is it possible to use Webhooks or Actions to accomplish this?

In my experience only dynamic form rules can work "on the fly", and they are not present during grid edit. Webhooks can only be triggered once you save - in which case it would be too late to change a field's properties.