Each search engine caches their results, so after the actual content is updated, it can take any amount of time for a search engine’s cache to be updated as well.
As far as I’m aware, Itch (or any other site) can’t do anything about this. I think some search engines allow you to ask them to refresh specific sites, but I’m not sure of the details.
For your specific case, I wouldn’t be too worried if I were you. As long as your actual page has the right information, you will be fine.
Hope that helps