Elrond shares your concerns about Amarthiel and has asked Lord Glorfindel to deal with the matter.
'I am concerned, ${PLAYER}, as I am sure you are, by the capture of Amarthiel. Though she has been stripped of Narchuil, she may still pose some threat to the unwary.
'It is no small choice, deciding the fate of Amarthiel. But there are other pressing matters; strange news has come in from my scouts in the south. I must concern myself with these things, as well as others, and I have tasked none less than the Elf-lord Glorfindel with the matter of Amarthiel. See what counsel he can give you, and maybe you can offer him some aid in rendering his judgement.
'You may find Lord Glorfindel outside of my house to the south-east.'
Glorfindel can be found outside the Last Homely House to the south-east, looking out on the Falls of Imladris.
Elrond has asked you to speak with Glorfindel.
Delossad is south-west of Rivendell in Tâl Bruinen, east of Garbert's cottage.
Glorfindel has asked that you question Narmeleth in Delossad.