I have done that & yes it does melt fast or I am slow!!

My sewing room floor has this same pattern, thanks to our dog chasing the cat. At least we are getting ready to put down new flooring so I didn't mind too much.

Oh dear!

I can not tell if your carpet has enough nap to where you could just snip the tips of the damaged area away. do a very little spot to see if it will work. just a suggestion.

I have one on my bedroom floor was using a heavy industrial iron hand cramped and it fell to the floor burnt all the way to the backing, and of course its right in the middle of the floor. needless to say went and bought a small cheap iron for quilt presing and save heavy one for hubbys pants.

Just tell people it's your branding iron design...
(tee hee - couldn't resist that one -- I'm from Montana's cattle ranching country)

yup i've seen that before , so sorry