Miss Manners: If a grieving spouse thanks you for expressing sympathy, is it okay to say ‘you’re welcome’?

DEAR MISS MANNERS: Person A lost his wife after nearly 65 years of marriage. On what would have been their wedding anniversary a few weeks later, Person B texted Person A to say, “I’m thinking of you on your anniversary.”
Person A wrote back and said, “Thank you — it was a hard day, and I appreciate you thinking of me.” Person B texted back, “You’re welcome.”
Now, I know that “You’re welcome” is more polite than alternatives such as “No worries,” “No problem” or “Of course.” But it seems somehow inappropriate in this circumstance, and I can’t put my finger on why.
What is one supposed to say in this scenario? What should Person B have said, if anything, when being thanked for thinking of Person A?
None of this is my business, so of course I said nothing. But it did cause me to wonder.
GENTLE READER: The sentiment being more important than the form, Miss Manners thinks Persons A and B both acquitted themselves most graciously.
How fortunate for you that it is not your business.
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(Please send your questions to Miss Manners at her website, www.missmanners.com; to her email, [email protected]; or through postal mail to Miss Manners, Andrews McMeel Syndication, 1130 Walnut St., Kansas City, MO 64106.)