Mortar? coming loose under slate roof on garage

[questionsquestions1]

My garage has a vaulted roof with some old, fairly fragile slate on it. Under the slate, along each rafter there appears to have been something (mortar?) which I'm assuming was used to keep the slate in place. Most of it has come loose and fallen off (see picture).

Should I:

A) leave it alone. It must have started coming loose years ago and the slate is still in place. This way I also avoid the risk of damaging the slate in the process

OR

B) Replace it to give the slate a better chance of lasting? If so what should I use and how?

Thanks

This is backpointing - it's usually done in the place of a felt or breather membrane (i.e. to stop you having a draughty roof) not as a fixing mechanism. I'd hope that the slates have been nailed in place.