you could start by pulling the worn rug off...

then yule see how it is attached, as well as have a sample of what you
need to buy

I wouldn't change a scratching post until it fell apart.  A heavily worn
scratching post to a cat is like a comfortable pair of old jeans or shoes to
us- they spend years "breaking them in".

Here's a quote from Dr. Nicholas Dodman, the Director of the Behavior Clinic
at Tufts:

"Many owners change a scratching post when it is old and tattered. This is
dead wrong, as shredding indicate frequent use and that is exactly what you
want. Half the fun cats experience from a scratching post derives from
getting their claws stuck in the material and leaving wispy threads as
testimony of their erstwhile presence."

I'd buy another post- but keep the old one until the cats break in the new
one.  You might want to consider getting a few scratching posts with
different textures and orientations (vertical, horizontal, wedge) to provide
different challenges for your cats that will stimulate their interest and
enrich their environment.

Phil

http://www.maxshouse.com/understanding_scratching.htm

http://www.maxshouse.com/Healthy+Happy_Indoors.htm

http://www.maxshouse.com/Environmental_Enrichment.htm

Consider wrapping the post with sisal rope instead of using rug which is
less durable than the rope.

I have one scratching post where after 5 years I needed to replace the
sisal rope because there were 2 cats using it. Now there is only one cat
using it; however, the 2nd post holding the top platform is covered with
carpet and starting to shred because the cat discovered it a couple of
years ago. When that carpet is far gone enough I will be replacing it
with 3/8-inch sisal rope.

If you are set on using carpet... visit the carpet stores and ask about
remnants. Don't pay if they want to charge you. Instead, go around back
and visit their dumpster... you can usually find pieces they have tossed
out big enough for the job. With this "method" you won't have a choice
as to colour.  :-)