Is the problem in the way I "save for web" or in the website I upload to?

Hello community,

I have the following problem - I "save for web" product pictures which are then uploaded to an online shop. A requirement of the platform is to only upload JPGs so I use the "high" setting and generally do not touch anything else on the default save for web settings.

When uploaded, the website puts a watermark over them, so I guess they go through second procession. But on a mobile phone they look quite compressed and fuzzy.

Since the client is throwing a fit over how that's my fault, I wanted to check what you all think...