Hello,
first all, we have to have a look on the RGB565 color space - and in a second step, we can have a look on your display.
In general, some slight green appearing gray colors are caused by the different color granularity of the color components red, green and blue in case of RGB565. The green channel has a higher resolution compared to red and blue.
When you take a black to white gradient you have the following colors:
#000000FF...#030303FF:
R [00 ... 1F] => 00
G [00 ... 3F] => 00
B [00 ... 1F] => 00
#040404FF...#070707FF:
R [00 ... 1F] => 00
G [00 ... 3F] => 01
B [00 ... 1F] => 00
#080808FF...#0B0B0BFF:
R [00 ... 1F] => 01
G [00 ... 3F] => 02
B [00 ... 1F] => 01
#0C0C0CFF...#0F0F0FFF:
R [00 ... 1F] => 02
G [00 ... 3F] => 03
B [00 ... 1F] => 02
The first gray value after black has slight green value of 1, but the red and blue components are still 0. The result is a slight green appearance.
This Image shows the color gradients in RGBA8888:

This image shows the resulting gradients in RGB565:

However, the described effect is not really noticeable.
Now, having a look on the photo of your display, the effect is a different one:
In your case, the higher red green and blue values are very saturated - and the lower values are missing.
Can you try to adjust the gamma values for your display?
Best regards,
Manfred.