First thing anyone will ask is what type of leather?
You don’t know I take it, neither will the customer no doubt.
Therefore you perhaps need to pass this over to someone locally to yourself that undertakes such jobs
Why not give Judy at LTT a call. She could advise someone in the locality who could give a professional understanding of how to sort your customers problems. I respectfully suggest it is not something your customer should try to do hoping it might look better but no worse. And if you were to try and fail then you could be the owner of a leather chair you never wanted.
Depending on how much grease and type of leather it can certainly look worse.
grease cannot be removed by cleaning only, and more often than not, even with using specialist products to remove the grease, restoration work is also required.
I agree with Joe, contact LTT who can sell you the de greaser and advise.