If you can write with EEPROM.write() or EEPROM.put() you can now just read it with EEPROM.read() or EEPROM.get(). You can read it every time you want to check if that position was passed. No harm in reading EEPROM often but it is a bit slower. So I would read the EEPROM into a variable in setup() and use that. Don't forget to update that variable as well when you save a new value to EEPROM.