All right, I got this working on 4.4.3. All steps are the same as outlined in the OP, aside from these minor changes:
This file
Code:
/skin1/modules/Gift_Certificates/gc_admin.tpl
Is located in your site's skin directory, either
Code:
/skin/common_files/modules/Gift_Certificates/gc_admin.tpl
or
Code:
/skin/YOUR_SKIN/modules/Gift_Certificates/gc_admin.tpl
And this step:
Code:
{include file="currency.tpl" value=$giftcerts[gc_num].debit}/{include file="currency.tpl" value=$giftcerts[gc_num].amount}
should read:
Code:
{currency value=$giftcerts[gc_num].debit}/{currency value=$giftcerts[gc_num].amount}
The edit link appears in the Gift Certificate screen as shown in the attachment, and when clicked, changes the "GiftCert ID" and "Rem./Amount fields" into editable fields. One thing to note, is that the Amount field can not be changed to anything larger than the original value of the GC, but anything equal to or less is fine.