For labels that are clearly asking to be removed, the answer is YES, remove them. These labels can impact the recyclability of plastic containers because during the sorting process the labels can mask the type of plastic resin the bottle is made from, which may result in the bottles being missorted and/or not being recycled. 

Normally, labels on plastic containers aren’t problematic and can remain on the bottle, jar, jug or tub.  Most labels are either recycled with the container if it’s the same resin or handled by the reclaimer.  So, if you see a bottle, jar, jug or tub with a label that asks you to remove it, please do!  Put the label in the trash and the bottle, jar, jug or tub in the recycling.