TESS Input Catalog versions 8.1 and 8.2: Phantoms in the 8.0 Catalog and How to Handle Them

We define various types of "phantom" stars that may appear in the TESS Input Catalog (TIC), and provide examples and lists of currently known cases. We present a methodology that can be used to check for phantoms around any object of interest in the TIC, and we present an approach for correcting the TIC-reported flux contamination factors accordingly. We checked all 2077 TESS Objects of Interest (TOIs) known as of July 21st 2020 (Sectors 1 to 24) and sent corrections for 291 stars to MAST where they are integrated into the publicly available TIC-8, updating it to TIC 8.1. We used the experience gained to construct an all-sky algorithm searching for "phantoms" which led to 34 million updates integrated into TIC 8.2.