I see this as a Doppler effect on the light wave caused by either decompression and/or compression. If it gets red as it approaches the blackhole, I would bet that the further away it gets the bluer the wavelength.
What is the % shift created by the gravity and what is the % shift created by the change in speed of the star?
Since the star is at a right angle to our line of sight, its speed is irrelevant..................