These links are enabled by default, to allow a more seamless registration for the scenario where the same registrants is registered for multiple quantities or multiple events within the same event transaction. 

Hiding these links would require a customization written by a web developer, either at your organization or through our Professional Services team for a billable service. How do I make changes to the design on my site?

How to make an event registration form auto populate registrant information when more than one event is available?