marfilh
Over the years I've had several remotes for several devices where the batteries have leaked like that.
I've always been able to put them back into service by scraping the contact points with the battery (spring at - end, solid contact at + end) with a screwdriver, nail file, etc., so that they again make good contact with the battery ends.
If you're unable to rejuvinate the remote, you can get a replacement remote from Roku, or many retailers. For a Streaming Stick, you'll need any of the Roku Voice Remote models. Infrared universal remotes cannot work with Streaming Stick models.