The answers is that deleting tag history is not supported.
I also wanted to know if this is possible, so I contacted Tumblr Support to ask them.
For reference, this is the response I got from Dave at Tumblr Community Support;
Thank you for reaching out and asking about this.
That's not supported at this time, but thanks for asking about it. I
contribute regularly to reports that my team puts together to make
recommendations to our engineers, so any time you ask for something
new, that’s super helpful to me. Though changes aren’t up to our
department, we do make sure that every suggestion gets passed along,
and I know that the decision-makers at Tumblr do read and care about
This is the screenshot of the email;