Editing out the word over isn’t hard to do. Test the sentence to see if it can work without it. Most instances, it can.
Don’t: I shoved the tray over closer to her.
Do: I shoved the tray closer to her.
Don’t: She slid over beside me.
Do: She slid beside me.
Don’t: I sauntered over to the center of the room.
Do: I sauntered to the center of the room.
In these cases, it’s a filler word and can be struck out. A lot of times we feel it shows direction, but the sentence is clear without it.