If you pour a glass of wine for a guest and discover a piece of cork floating in the wine, replace the glass and pour some wine into it.
Do not just pick out the cork with a spoon or fork and tell them it will not hurt the taste. You may do that at home for your own personal wine drinking so as not to waste the wine, but a guest will be more concerned about bacterial, mold, or taste contamination of the wine and may be offended if you just offer to remove the pieces of cork.
If the guest insists on not discarding the wine with the cork piece(s) floating in it (perhaps it is a bottle they brought and are paying corkage on), offer to take the glass and/or the bottle back to the bar or kitchen.
Pour the wine thru a cone-type of coffee filter or a very fine, clean metal strainer, into a decanter or other glass vessel to remove the cork. Then return and pour the wine for the host and check that everything is suitable for their taste.