While the surface area is a little larger than something like a cigarette burn, we are able to resolve iron burns in a similar manor by utilizing a process called bonded insert.
We start by cutting out the damage caused by the burn using a sharp utility knife. A donor piece of carpet would be made to fit into the repair space, trimmed exacting to size, with the orientation to carpet direction. Finally, we bond the donor carpet into place using a special micro wave tape.