At this time the ability to get payment.updated webhooks for just payments created by payment link isn’t currently available. We’re constantly working to improve our features based on feedback like this, so I’ll be sure to share your request to the API product team.
Are these payment links created in the Dashboard or your application. If it’s with your custom application you can filter all payments by your application ID. Any payment with your application ID in it will be one that was made by payment links. 