Eyelet tape
I wonder if this is what you are looking for:
It need not have metal eyelets in it - it could be more like broderie anglaise.

http://www.caltrims.com/eyelet-tape.php

This is not at all easy without a picture, and I don´t suppose you have one!

If you really can´t see what is meant or ask the client, you may have to go for a blanket term like ´border trim´.
There are lots of possibilities!

ALTERNATIVELY,
There is something called hulbånd here, most easily visible on the blue and grey model. (Click to enlarge)
http://www.outnet.dk/da-the-north-face/base-camp-travel-cani...

That just might be used as a trim on a top or blouse.

A third option:

The other kind of ´hulbånd´ is something from a builder's merchant, and although that is NOT what you would find on a garment - it is a metal strip - it looks like a double row of ric rac braid, and might just be something like this:

http://www.ribbonmoon.co.uk/details.asp?id=22481
(Product EO52, WHITE ELASTIC WITH A METALLIC RIC RAC BRAID)
_____________

But if you cannot find anything specific, I would go for a generic term.


--------------------------------------------------
Note added at 2 hrs (2011-04-19 12:01:57 GMT)
--------------------------------------------------

Try scrolling through some of the eyelet laces here - I think this might be quite a safe bet!

http://www.caltrims.com/eyelet-laces.php

I checked my sewing guides from Singer, and the only neck lining I san find is "interface" which is produced in many different types.

--------------------------------------------------
Note added at 1 day7 hrs (2011-04-20 16:36:01 GMT)
--------------------------------------------------

"I san" should read "I can"
- sorry for the typo.