Moss on thatch

This is usually caused by the roof being in a windless, damp, north facing area and is not a rare happening.

The presence of moss is not necessarily detrimental to the thatch. It can in some circumstances appear unsightly. If required it is always desirable for a thatcher to remove the moss by the best means he considers. Some success has been reported on the use of a copper strip on the apex.  However:

The most effective method I have found is the application of one of the garden path moss/algae cleaners, spray on as  directed for a path, Or Wickes (the builders merchants) do a mould inhibitor. I cannot advise the use of these for legal reasons, It is what I do to mine however with a mask and goggles ! Try and keep off the roof with ladders, if you need to put a ladder on the roof spread the load with an old rolled up carpet or coir door mat under the ladder. Do not put any ladder on or even touch the ridge or areas with rods and spars.  The scaffold design for your access would be the same as that on a tiled roof. The important points are to keep operatives off the roof as much as possible, in particular the ridge and to protect the scaffold supporting points where they rest on thatch. Traditionally supports were protected by straw filled sacks. Old rolled up carpet is a good alternative. If any pointing, flue lining or rebuilding is expected it is important to prevent mortar debris getting onto the thatch, apart from being unsightly the lime can damage the thatch. Plastic sheeting right down the roof is essential. Allow for drips & leaching out over plants (& humans! - why I do not advise you do it) under the eave.

This may require two applications a year and it will probably come back - just repeat the dose and do in damp weather or the crust may break and damage the roof.
I am assuming  that the moss is a khaki colour slime mould lichen type (may have an ' Elks antler ' up to 1" vertical leathery growth) or just a light sticky covering.

If it is dark green and a thick mat of cushion type growth is allowed to develop over 1/2" thick it can trap water and prevent the roof from breathing it will require removal, try (after spraying and waiting) removal of a small area to test, Without removing the netting (if any) if more than 1/4" of the thatch surface comes away with it contact a thatcher for advice, the one who thatched it if possible. Do not just rip it off, you will damage the roof. Even more important if it is a long straw roof   Brush off with a garden cane or broom.

Power sprays can be used for application, do not unless experienced use for removal, always use down the roof, never point upwards.