First thing to try is a cotton bud dipped in undiluted washing-up liquid and gently rub the area that is marked. If this removes it then use a soft cloth dipped in a solution of warm water and soap, well wrung out so that it's just damp and wipe the screen gently across, buff with a clean dry cloth.
None of the above will cause any harm to the screen. But if it doesn't work then you could try with caution and I can not guarantee it will not harm the screen, either of the following.
1)A soap like tablet with the name of "Vanish" This is excellent at removing stains of all kinds but of course I've never heard of it being used on a TFT screen.
2) WD 40 will remove ink from clothing and other surfaces without any damage and is excellent for removing that sticky residue that labels sometimes leave behind, then finish with soapy water solution as above.
The first method as I mention above can be used with confidence. The second two are something you must decide for yourself and are only suggestions on my behalf.
Good luck and let us know how you get on. j.