This can be managed with a custom field.
For example, you could create a checkbox field (e.g., “Unsubscribe”) and add it to the form. If someone selects the checkbox and submits the form, the value will be saved in Salesforce. In your Salesforce org, you can then update the list view filter to exclude any records where this checkbox is marked as true. This ensures that clients who opt out will no longer receive update requests.
Steps for this Configuration:
1. Go to the Contact object (you can follow the same steps for Account and Lead objects as well).
2. Click on Fields & Relationships → New.
3. Select Checkbox as the data type → click Next → fill in the required details. 
4. Click Next, Next, and then Save.
5. Navigate to Contact object → Field Sets → Edit "ContactDetails" field set and add the Unsubscribe field.
6. Repeat the steps 2-4 on the Contact Update object (you can also do this for Account Update and Lead Update objects if you want to configure for those as well). 
7. Go to the "About Update Client Details" tab and in Step 3, Map the fields 
8. Go to Sites and open the site used for the Update Client Details app configuration.
9. Open Public Access Settings → give Read and Edit permissions for the custom fields created in both Contact and Contact Update objects. 
10. Once done, the user will be able to see the Unsubscribe checkbox on the form and can submit it; the value will be saved in Salesforce.
11. With this field you can add a filter on your list view to not show contacts who have unsubscribed to send the forms.