Category archive page isn't filtering by current category
Mystery solved; the relation code was too general; some of the entries were related to the category on the homepage, and the example code doesn't care about how or where the entries are related to the category as long as they are somewhere somehow.

I needed to be more specific:

{% set thingsToDo = craft.entries.relatedTo({
    targetElement: category,
    field: 'typeOfThing'
}) %}


Works.