But you've got bigger issue - your overflow tube is too tall. In case of a valve failure, water is supposed to dump into the overflow before it overflows the tank (and onto the floor). But your overflow tube is taller than the hole for the flush lever, so it's leaking through the handle hole before it reaches the top of the tube.

Remove the tank lid and examine the overflow tube. My guess is that someone's modified it to try to get bigger flush from a low-flow toilet - maybe adding a piece of hose or pipe to the top of it? Remove any extensions from the overflow tube, and adjust it's height so it's an inch below the lever hole. Some overflow tubes are height-adjustable. If yours isn't, you can easily cut it in place with a coping or hack saw.

Finally, bend the rod on the float so the water level stops a little below the top of the overflow. Many tanks will have an embossed mark indicting the maximum fill level.