The information on the Forge-master page is outdated.
When LIs were first introduced you could unslot the relics this way, it was later changed to the Relic Removal Scroll which was a Store only item. They recently made the Scroll available in-game as a rare drop and from Hobbit Presents.
As to whether to unslot a particular relic; that's really down to you. You will have to weigh the time and resources it took you to make the relic and the time and resources it would take to replace it against the use of a Scroll which, as previously said, is a rare drop or Store purchase. For high-tier relics it's usually very much worth it, for the lower ones possibly not, but then you may not have the resources available to replace them.
[center][url=http://forums.lotro.com/showthread.php?18699-How-to-get-help-on-the-Tech-Forums-and-how-to-contact-Turbine][color=gold]How to get help on the Tech Forums and how to contact Turbine[/color][/url]
[color=green]Please reply to the topic or PM me if a solution I posted works for you: The more data I can gather the better I can help.[/color][/center]