That screen needs a lot more cleaning & buffing since I cannot see anything else but smeared grime.
After using a damp cloth, you need to use a dry clean cloth to wipe up the remaining moisture & buff it out. You will need to fold the cloth a few times to find a clean dry area of the cloth to finish the cleaning/buffing process. For the grime shown in the picture, you may need to do this several times before the glass is clean.
You may actually need to use a bit of an LCD screen cleaner to get that grime off if my suggestion above doesn't work to remove that grime. Do not use any harsher chemicals or you will damage the coating on the glass.
If after cleaning the screen you still see the white spot, then see if you can use your fingernail to gently scrape over the white spot (since you felt it) so it may break up the debris so your cloth can wipe it away.
FYI, when applying water or an LCD cleaner.....make sure you apply it to the cloth so the cloth is only very lightly damp or you can cause liquid damage to the display (liquid can seep behind the edge of the glass to get between the glass & LCD panel causing permanent visual damage). I've never encountered any issues using an LCD screen cleaner on the recent Macs prior to the models with the Nano Textured screens....I have yet to encounter one of the Nano Textured screens so I would avoid LCD Cleaner with a Nano Textured display.