I just tested it on Edge and was able to remove a saved search. Please, make sure you follow these steps for a saved search you'd like to remove (I tested it with a search named "translation 2"):
On your Job Feed page, click on the name of a saved search and it'll open. Then you can click on the menu button at the top of the search and select the "Remove Topic" option.
This issue is still not fixed on Firefox neither Internet Expl.
I cannot install Chrome (will not explain why here).
So instead of telling us to use Chrome, you guys need to fix the bug.
Put check boxes and a delete button. So simple.
I don't use Chrome either (although have it installed on my Mac) as it tracks me even when I'm asleep . . .
I have a 'saved' job here that has been there for over a year - and not a bin in sight (in site).
This site should be compatible with any browser that a client or freelancer wants to use - even IE11.
Your recent searches should show under "Recent Searches," which is not visible on your screenshots. In order for your Job Feed to display relevant jobs, you need to save some searches. You can do it by running a search by keyword, applying some filters and then clicking "Save This Search to Your Job Feed" button: