How do I edit the links in a filter
This is an educated guess: 

The page "Programs &amp; Services" on the programs-services link is built by Views module. 

You can edit the Views by clicking on the small gear icon you see in the top right corner of the content area and choosing "Edit Views". Or find that particular View under Structure > Views and edit from there. 

Under Filters on the left you'll probably have several filters listed, with one of them labeled (exposed). You can click on it and Remove - that is how you get rid of the "drop-down" filter currently present above the results. 

To change which page titles appear in the results you again have to change something under Filters, but it's impossible to tell what because that depends on your site configuration. 

Sometimes (besides the Published filter) there is the filter based on Content type, for example, to list only Articles that are on the site, or only Basic pages. 

Sometimes there is a filter that filters by Taxonomy (tags) that the content is labeled with (for example list only content tagged with "Medical"). 

You need to find out what the current filter configuration is (post a screenshot), and how your new pages you want to list there differ from other content (are they of a different Content type, have they been posted after some date, by a different author, tagged with some tag). 

Then you'll be able to change the filters accordingly to show the new content instead of the current list.