Jonathan Crawford wrote :

It seems that your cat has trained herself to use the litter tray and
that is a possible reason for her using your doormat rather than do her
business outdoors.

The thing is there is no way around not having a litter tray.  My cats
rarely use the litter tray but I still got to have one in case they get
stuck.

All I can suggest is move the doormat and get a litter tray.

Start with a litter tray on your doormat....Then move it gradually (over
several weeks) to your garden. then replace it with four 1 x 2's forming a
square, with garden dirt beneath them........

You could provide a litter box outside to give her the understanding that's
were you want her to do it. Be glad you cat just potties on a mat if they
were
not provided an alternative. My bed would be were my cats went if I didn't
provide a box.=)

Hi Jonathan,

You really need to toilet train your cat as if she were a kitten.  In your
position, I would take 3 courses of action:
1.  While your doormat is still soiled, put it outside where you want her to
poop*; then introduce her to it.  Because it smells strongly of her, she may
start to scratch at it or around it.  If she does, praise her very warmly,
because this is the normal behaviour of a cat who wants to bury her poop.
It's precisely what you need to encourage.   *Do not put the poop mat in her
favourite snoozing place - she will be profoundly disinclined to use it.
Further, it will probably be a warm place where her deposits will reek
horribly!
2.   After each meal and each catnap, pick kitty up and take her outside to
use her new pooping spot.  When she uses it, praise her ... when she doesn't
use it, also praise her so that she associates this very personal site with
your warmest approval.  (Eventually, you may be able to remove the mat,
again leaving some poop as a marker for her).
3.  As soon as you can after the poop mat has been resited, clean very
thoroughly inside the doorway where she used to poop, removing all trace of
her scent, otherwise she will feel a natural urge to re-mark this spot.
Also, you need to consider any odours you bring into your home.  If you are
leaving soiled shoes by the door, she may be able to detect another animal's
scent and her natural reaction to that scent on her territory will be to
overmark it with her own scent.  This isn't naughtiness or perverseness -
it's essential to her sense of security.  It seems certain that she does
feel insecure, hence her need to return indoors to poop.

In the early days, she may still try to poop by the door.  If she does, say
NO very firmly and take her outside to her poop mat.  Praise her simply for
being there .. even though you had to put her there yourself.  Slowly but
very surely, you should see a change in her behaviour.

Do let us know how you get on.
Spider