In the situation you describe it's irrelevant that you do not intend to make money by distributing your cards. Your proposed use would be an infringement of Geisel-Seuss Enterprises' copyright in the Grinch image. Moreover, your proposed use IS an effort to make money by using the image because you'd be distributing the cards to your clients (the purpose being to market your services to those clients).
In addition to copyright infringement, your proposed use of the Grinch image (and the word "Grinch") would likely also infringe the trademarks that Geisel-Seuss Enterprises owns in the image and word "Grinch." See http://bit.ly/7QooOA and http://bit.ly/4XaIuy .
Whether your use actually gets you money isn't the point, as your use is clearly promotional and commerical to benefit your business, and infringes the rightsholder's rights in the image, trademark and character you want to use.
You may also be infringing the rights of the owner of the recent film, if your image is taken from that work.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.