The “net” is called a lip or lingual brake:
Lip brake: a small attachment connecting the lip (top and bottom) to the jawbone
Lingual brake: an attachment that connects the tongue to the jawbone
We perform a frenectomy only when the position of the brake causes slurred speech, loosening of the gums, dental malposition, etc. It should be noted that postoperative pain is minimal and most of our patients are able to resume normal activities almost immediately after surgery.