We've reviewed your book and we're not sure why the company is objecting.
No copyright, no cry. We believe that the failure to include copyright notice placed the flyer into the public domain, making it available for anyone to use. For works published before March 1989, authorized publication without notice typically doomed works, unless excused. (By the way, the U.S. was the only country following this rule.) Even if the flyer were not in the public domain, you have one of the stronger cases for fair use that has crossed the Dear Rich Staff's desk. Only one of the four fair use factors -- the amount and substantiality of the portion taken -- weighs against you. Otherwise, your reproduction of this 35-year old advertisement is highly transformative and should not deprive the $13-billion-a-year chain of any potential market share.
Trademark rights. A company can object if its trademark is used in a manner that confuses consumers as to source -- for example, consumers believe your book is sponsored or authorized by Trader Joe's. This is unlikely considering your prominent disclaimer and your failure to include the company's distinctive lettering or logos. Further, as we've written before, the use of a company's trademark is permitted for editorial purposes, which is clearly the case here. We also don't think there's any trademark dilution.
Bottom Line Dept. It's difficult to understand why the grocery chain is objecting to your book, especially considering how TJ-positive it is. We can only chalk it up to too much Cookie Butter.