Filter out headers from a table of contents

Dear community,

I'm have some inline TWIG code on one of my markdown webpages to print a table of contents exactly where I want it (instead of using the default plugin option). It works great, but it includes some headers that I'd like to filter out.

{% set table_of_contents = toc(page.content, 2, 4) %}
{{ table_of_contents }}

I can't filter out the headers through choice of included header level because that removes headers I want. I'd like to filter by string. Let's say there are two headers I'd like to filter out "Header 1" and "Header 2". How would I adapt the above code to remove those headers? I looked up filters in GRAV documentation but I didn't seem to find one that would suit my needs.

Thank you,

Sean