The gform_web_api_capability_delete_entries filter in Gravity Forms allows you to change the capability required for a user to delete entries via the web API.
Usage
add_filter('gform_web_api_capability_delete_entries', function ($capability) {
    // your custom code here
    return $new_capability;
});
Parameters
- $capability(string) – The capability required. Defaults to ‘gravityforms_delete_entries’.
More information
See Gravity Forms Docs: gform_web_api_capability_delete_entries
Examples
Change the capability required to delete entries
Change the capability required for a user to delete entries via the web API to ‘delete_others_posts’:
add_filter('gform_web_api_capability_delete_entries', function ($capability) {
    return 'delete_others_posts';
});
Allow administrators to delete entries
Allow only administrators to delete entries via the web API:
add_filter('gform_web_api_capability_delete_entries', function ($capability) {
    return 'manage_options';
});
Create a custom capability for deleting entries
Create a custom capability ‘custom_delete_entries_capability’ for users to delete entries via the web API:
add_filter('gform_web_api_capability_delete_entries', function ($capability) {
    return 'custom_delete_entries_capability';
});
Allow editors to delete entries
Allow editors to delete entries via the web API:
add_filter('gform_web_api_capability_delete_entries', function ($capability) {
    return 'delete_published_posts';
});
Restrict entry deletion to a specific user role
Allow only users with a custom role ‘entry_deleter’ to delete entries via the web API:
add_filter('gform_web_api_capability_delete_entries', function ($capability) {
    if (current_user_can('entry_deleter')) {
        return 'gravityforms_delete_entries';
    }
    return 'do_not_allow';
});