"googler" wrote:

I made a mistake of keeping a hot iron box on the carpet and that left
an ugly mark on the carpet. I am looking for a good idea as on how to
deal with it,

As of now, it looks like replacing the part is the only option. I am
not sure how to replace a part of the carpet. Since this is on the
stair case, i am assuming that laying a new piece of carpet does now
show up badly.

See if you can find a carpet sample from a closet. Have a carpet installer use
that carpet for the repair and replace it with something similar.