pic16f628a
Hmmm, bad news for you. Probably (a strong possibility) that all 16F628A used in your boards are code protected for reading, so you will not be able to read, study and modify the code.
Even if the PICs are not protected, you should have a PIC programmer (a special hardware connected to PC) that can read the code inside the PIC and a software (controlling the programmer hardware) that shows you the code (in assembly language). You should know PIC assembly language to modify the code. If you manage to do it, the writing process in to the PIC is the easiest part of the whole process.
Look for MPLAB software (free) and PICSTART or ICD2 programmers, both from Microchip (the PIC manufacturer). There are similar programmers also, manufatured by third parties, cheaper than Microchip ones.