The likelihood of this change making a + / - difference in the rank of your category page is very low.
At best, the weight an H1 has in on-page SEO falls solidly into the bottom half of all factors affecting page rank. Further, based on the theme preview, there is very little on this template to generate search rank in the first place. The vast majority of the content is dynamic, and though it's related by category, the actual snippets of copy associated to the content this page touts aren't topically connected.
Given the page's utility, which is to coalesce category-related content, your priority for this page should be to ensure that it does its job, which is to move visitors through to actual content. You don't want a page like this to become a bottleneck. Without changes to the template that result in engines having more unique information about this page, that's the best you should hope for here, IMO.
The two primary, static elements on this page are the main heading and page title (there may be others that don't change). They should be tied together in terms of what they communicate about the page. Regarding the removal of the word "Browsing", its presence or lack thereof will have very little, if any, impact to page rank. In terms of how this word choice affects the page's key performance aspect (to get people to other content), it pretty canned, but that's just personal opinion.
