Google's John Mueller felt the need to post a PSA that said having an incorrect date set in your last modification date within your HTTP header won't hurt your SEO. He said on Mastodon, having an incorrect date set there "won't negatively affect your site's overall SEO if used wrongly."
John wrote about spotting an article that said otherwise. He said, "I ran into an article about the "last-modification" date HTTP header, which claimed it would be bad for your SEO to have it set incorrectly (specifically, always set to "now') by plugin."
John said nope, he wrote, "This is not the case, it's not bad for SEO. Yes, it's good to use last-modification date headers appropriately, as this helps with crawling efficiently, but it won't negatively affect your site's overall SEO if used wrongly. Your site won't rank lower."
John then linked to Google's official documentation on crawl budget management for large sites and helping Google know your dates.
Here is a screenshot of those tweets:
Forum discussion at Mastodon.