Is there a way to get rid of or remove non-giftable items such as Limited Edition Loot?

Once you have items that are not giftable like Limited Edition Loot (LEL), you will have them forever (or until Zynga changes things.) This means you can't trade LEL and you can't discard it either.

Unfortunately the main consequence is that (other than never being able to get your hands on some of the neat LEL of yesteryear!) if you've purchased a lot of LEL that overrides the equipment you want your mafia to use when attacking or defending, you have no choice about using the LEL. Unless you get something else that can override the LEL, you are stuck. It also means that if you want to purchase LEL released sometime down the line, there is no way to wind back the number of mafia members you'll need to purchase it -- you will have to add to your family to purchase the quantity of LEL you want.

So yes, you can wind up saddled with a number of weaker items that crowd out better equipment you have and want to use when fighting (attacking or defending.) Remember: although the game chooses items with the highest attack (when attacking) or highest defense (when defending), it's the combined total of attack + defense that determines an items combat strength. See this FAQ about determining whether or not to purchase LEL.

Don't fret too much about it though. Even if you have a lot of weak LEL that you are stuck with, by placing points into Attack and Defense you can deemphasize the impact your equipment has overall. Similarly, unless you are have hundreds of LEL that are much weaker than what is available to you through other means, it might not be impacting your combat score that much.

The soundest advice I can give is to place skill points into Attack and/or Defense (a good strategy regardless of your equipment situation) and do your best to acquire any drop loot that can push out the LEL, if any is available. And maybe keep your fingers crossed that Zynga will release some new uber-LEL! :)