Water can collect under the plastic shield and other components which prevent the buttons from working properly or at all. You would be best to open this anyways as rice will only help to remove some of the water, but not all and what is left behind are usually mineral deposits and starch from the rice. Stay away from rice as much as you can. It is always best practice to open the device and clean all remnants of water if possible.
I don’t think there are any screws. The remote is made up of two halves that snap together. You will very likely have some pry marks when done. Find the seam between the two halves and gently pry until it snaps apart. This made me very nervous as it was held together very well. I did not need this but keep some super glue handy just in case the two halves do not snap back together fully.
Note: The IR cover on the front of the remote can fall out. It is only oriented one way but I wanted to let you know it is not held in place when opening the remote and to make sure it is in its proper place before reassembly.