I prefer to use variables over global switches personally, but I digress.
Here's one way to do it with self switches. Self switches are not global, so they'll only affect things within the event they are called.
Basically you just add a self switch at the bottom of your event.
You can find it here... A, B, C, or D is fine.
Create a new page
within the event you're working on and use the page conditions to look for that same self switch.
If you're just using this method to get rid of an event, then leave this page blank. The event will vanish once it is done and will not run again.
To be clear, this method will get rid of the event immediately after it has run its course. If you want the little girl to dissapear only after the player has found this cat. Then you will have to make some slight changes. Instead of using a self switch, you may use a normal switch (first option under Game Progression). Place the ON Switch within the cat's event, but set up the blank page within the little girl's event the same way. Now once you've interacted with the cat, the girl's event will switch to the blank page and appear to vanish from the map.