Plant stains can be a combination of several components. As a plant is over-watered it will run out of the pot and onto the carpet, saturating the carpet beneath. On its way through the potting soil the water can pick up all sorts of minerals, soils and dyes that can be difficult to remove. To make the situation worse, if the potted plant is in a basket the water can pick up tannin and additional dyes.
The worst part about plant stains is the fact that the water will remain under the pot for extended periods, providing and excellent growth medium for mold. The mold will do more than stain the fibers. It can actually eat away at the fibers of the carpet and backing, assuming that there is anything organic to be consumed.
Once the plant is removed and you are asked to remove this stain it may too late to do a really effective job. Be sure to qualify the situation with the customer and do not offer guarantees.