Roger – Without knowing what your particular by-laws are a door mat could offend a couple of by-laws such as: not leaving belongings on common property; not changing the appearance of a lot; not installing anything that could cause a safety hazard for the common property or the Lot; and not reducing the level of fire safety for the building.
However, common sense should apply.
Do a quick check of the building to see if other apartments also have a doormat. If you see other door mats then you should be OK. If you don’t …. then you may have a problem.
If your door mat was a safety issue then it will be noted on the next health and safety audit for your building and there would be a justifiable reason for you to be asked to remove it.
The following article provides a warning about trip hazards in strata:
https://lawyerschambers.com.au/owners-corporation-ordered-to-pay-150000-to-injured-lot-owner/