remove page/secondary header

hey guys and gals! i only have been lerning wordpress for about 4/5 days now and am working on my first blog ever, so bare with me if i cant explain my question in great detail. basicly, im running the catch box theme. my blog is mainly divided in two categories, wich can both be accessed from the main menu. however when i select one of the categories from the menu, the theme by default has something like a secondary header or so (i really dont know how its called) and i would like to delete it. when im on the frontend of the page, right click on this header and select ‘inspect element’ it shows the 1/2 lines of code for the header and when i delete them, this page header disapears aswell. obviously when i refresh the page it comes back! so basicly, since i know wich part of the code i have to delete, is it secure to just delete it on the backend? will it mess up any future updates, or will it just come back in future updates? and if it is secure to delete, where do i need to go, to delete it?

if you want to see what im walking about, the site is playittwice.com (still very basic, dont make fun of my wp skills yet), the two categories are music and production and when you select one of those, what i mean with second header is the smaller black box that says ‘CATEGORY ARCHIVES: music/production’

thanks in advance for any feedback