Thanks Carol, I'll let it do its thing for now :o)

Reasons to remove : To avoid the rot. To remove the residence of insects.

If it were me, I would cut those tips off. Like four said, you want to avoid rot. The cuts will allow more branching.

I actually agree with both of you, now that I've had a little time to think about it. My answer wasn't very clear, and I apologize for that. I was thinking wait a bit to see the extent of the damage before trimming, and I should've stated so.

Thanks All for all your help and advise, I ended up calling a Plumeria Nursery and she did say to to cut the damaged tips to the point until I see white/green healthy part, till I couldn't see any rot and cut another 1/4 inch below that to be on the safe side.

Hopefully it will get new growths in a few weeks, fingers crossed! Thanks again!!