Hello
I made a neck edge in a similar way recently.
You don’t pick up any new stitches along the back.
It feels a bit strange but just knit the 3 stitches, turn work the wrong side 3 sts, turn, work the right side 3 sts… and so on. Keep going until you have a long thin strip. This will join to the 3 stitches in the other side of the neck.
Have a look at your finishing or assembly instruction or possibly the following part of the neck band section, it probably says to sew the neck band across the back of the sweater.
When I did mine I made it roughly as long as I thought I needed and then began sewing it in to the back neck piece to make sure I didn’t make the strip too short or too long. You want some stretch and give in how it matches up with the back neck. Joining to the back neck can initially be a tacking stitch with a thin sewing yarn or embroidery yarn to just hold it in place if you want to be able to remove it and do the real seaming with your proper yarn afterwards.
When knitting it feels a bit pointless having just 3 stitches but that little edge will finish off the sweater very nicely.