Your control has TV parity checking, but it's usually turned off. Very few people use TV parity checking anymore. TV parity is just checking to see if the number of characters within a block are even or odd. If it's odd, you have to add a space character to make the number of characters even.
If this is a 5T control, move the address LED under the "SET" position, and look for a bit under the "TV" position. It should be "0". If it's not, set it to "0" in MDI and press INPUT. On later controls, the "TVON" bit is on the SETTING screen.
A TH (Tape Horizontal) parity alarm is different. That usually means that you're trying to send the CNC an illegal character, or your baudrate or stop-bits don't match.