Hello, A.
The HD44780 interface datasheet lists two different sets of characters. The last time I checked, the LCDs we sell come with the first set of characters (which includes Japanese), not the second one where you saw the 0xB0 character. You should be able to get a character that looks like a degree sign by printing 0xDF to the LCD. Inside a C string, this can be written as “\xDF”.
–David