Just purchases a CX5 Sig and my back seats look terrible after one week! I gently wiped them down with a damp soft cloth to remove some dirt, and they look like they've been wiped down with something that should not have been used. Marks all over them.

Any advice to clean them up, get them looking new again?

 

While under warranty, you should use what Mazda tells you in the owner's manual.
Non-toxic cleaners/conditioners, whatever that means.
If you wipe them down with a damp cloth you need to wipe them immediately after with a dry cloth.
Any dampness from clear water or any cleaner will leave streaks or residue.
I use the same brand leather cleaner/conditioner that I used on my custom-made leather motorcycle jackets/racing leathers for decades.
It works great and kept the leather looking new, but I won't recommend the brand that begins with an "M" as they are all opinion subjective by the user.

 

Do not use any leather cleaners or conditioners that have alcohol as an ingredient.
Always wipe excess conditioners off because unless you have tinted (with film) windows the UV will intensify and wear of your leather that have the high luster shine.