This is a bug. No two ways. You should NOT have deleted posts show up in the feed. It’s a deal breaker for us.
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Hi there and welcome to the Community! 
Thank you so much for your feedback!
I completely understand your point, and I agree that it would be great if deleted posts could be removed from the widget right away. However, since our Instagram Feed app uses a cache system, it’s not possible to immediately pull new posts or remove deleted ones.
This is the expected behavior due to the cache system.
We’ve already submitted a request to implement automatic deletion of removed posts, and you can upvote it here - Remove deleted post from the feed automatically
If you ever need to remove deleted posts in the future, feel free to reach out to us. Our dev team will be happy to assist you! 
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