Couple of things…
If your employer or a recruiter for your employer has a LinkedIn Recruiter premium account, they can search by this entry.
Here is what I got from LinkedIn Answer page explaining this :
Important: In order to protect your privacy, we’ll make every effort to hide you from Recruiter users who may also work at your current company, as well as related companies. Learn more about privacy for shared career interests and how to update your current company.
Not entirely true but its always good to be a little careful about that.
Just click the up/down arrow next to the job entry you want to move. Then hold and drag the gray vertical bar.
In the latest LinkedIn UI update, this no longer works. LinkedIn automatically sorts them according to ending month (most recent first) and you get a blue burger bars only on the items that share the same end month.
Heads up, people! You can deselect the “notify your network” option, for a while or forever, while you go about your private updates under cover of darkness. Then turn it back on when you have something important to share.
Again, in the latest version, you will be asked if you want to share each new information you add to your profile (there’s a slider at the bottom of the pop-up). Edits to existing entry will not show up as an update.