It could be that you're simply not getting enough flushing action through the carpet. I think if I remember from your posts elsewhere, you run a portable? What sort of spec is it? You may have to be prepared to do the whole thing again, and spend a lot longer rinsing it through.
This may be one instance where a microsplitter or colloidal and cold water rinse would really outperform any detergent.
If you think about it from another angle... how do you get a nice cup of traditional English navvy's tea? Stew it for ages! A well stewed cuppa leaves tea stains behind in the cup, so transferring that back to your carpets... if they had dry tea in them and you wetted up the tea for what was probably a good few hours, the carpets are going to be experiencing something similar to your favourite tea cup with the scummy tea marks inside it.
Also, when a cup of tea is spilled on a carpet, if it's hot the problem is often a lot worse. The dye sites are opened up, allowing the offending substance to migrate further into the fibres. Fortunately this is likely to be a polyprop carpet and not a domestic woollen one, so this is less of an issue. But, if you've rinsed this carpet with hot water you may have exacerbated the problem nonetheless.
Pre-vacuuming mustn't be overlooked either. What vacuuming procedure and machine did you use on it prior to wetting it?
I'd attack this with a really thorough vacuum, generous application of M-Power (other colloidal agents are available), a good old scrub with a rotary and brush and then a long dwell time. Cold water rinse, very thoroughly, partially dry off and then lightly spray up again and bonnet to finish with.
How much area are we talking about?