TNR stands for Trap, Neuter, Return.
 
It is the process by which stray or community cats are trapped, taken to a vet to be spayed/neutered, vaccinated, and eartipped, and then returned and released to the same area in which they were trapped. 
Alley Cat Allies, an expert in the field of TNR, has a wonderful website dedicated to teaching the public all about TNR. 
Learn about TNR and WHY IT WORKS. https://www.alleycat.org/resources/why-trap-neuter-return-feral-cats-the-case-for-tnr/
Learn ALL ABOUT THE VACUMN EFFECT and why you can't just remove the cats. https://www.alleycat.org/resources/the-vacuum-effect-why-catch-and-kill-doesnt-work/
What is an EARTIP, and why is it important?
 
An eartip is the removal of the top 3/8" of one of the cat's ears (which ear depends on the gender of the cat and the region you are in), and it indicates that the cat has been spayed or neutered as part of a trap-neuter-return project. It's done painlessly under anesthesia, and is an essential part of TNR. It is an immediate visual cue that indicates to trappers and animal advocates that community cats are already sterilized, and protects them from being trapped again and in many areas protects them under the law from being picked up by animal control and impounded or euthanized. 
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Watch this super cute video from Kitten Lady to learn more about EARTIPS...
What does the law say about community cats?
Community cats are protected under the law in Orleans Parish as long as they are eartipped or microchipped, signifying that they have been spayed/neutered. Please see Municipal Code/Ordinance Section 18-14 HERE to learn more.