Is there a recommended carpet cleaner who is willing to give a free estimate?

I've recently had a problematic airbnb guest who has managed to tread a large piece dark brown eye crayon into my cream carpet.  It's a small stain but very noticeable.  I'm claiming for damages from airbnb to clean the carpet but in order to do this I need to present an estimate from a carpet cleaner on headed paper.  I contacted the guy I usually use who wanted to charge me £20 for this quote even though I pointed out it could all be done by email if I sent him a photo of the damage and the measurements of the room.  I think this is a bit cheeky, so I'm looking for a carpet cleaner who would be willing to give me this quote free if I supply the information/photo online.  In return I can guarantee the work if and when I get the payout which should be resolved within a week.  Any ideas please?