Peat and Diesel are a fairly new band in the great scheme of things.

However, I reckon they will probably have enough "savvy" about such things to have made a considered decision whether or not to record and perform this song. So, I assume(and hope) that they have and will comply with all the legal aspects involved.
It might be that they aren't necessarily particularly concerned about royalties as far as this particular recording is concerned and just see it as a bit of fun and a chance to gain some extra exposure. I don't know.

As far as Kirsty is concerned, she was a wonderful musician and lovely person who was taken away from us too soon. I also think of her at this time of year.

However, I don't really think that the boys are taking the mickey out of the song but, rather, themselves and some aspects of their own local communiity albeit in a light hearted affectionate way.
It is a very gentle parody and is not intended to be offensive. I'm sure Kirsty herself would have loved it and seen the funny side and(I don't know ) Shane McGowan is probably having a smile too.

Finally, I believe that "Fairly Tale of New York" is much more than a shrine to the late Kirsty McColl. It was already a perennial classic before her untimely death and would have stood the test of time regardless.