They're making claims of performance. +15kts cruising speed, 4*C or 1200 lbs in hot/high take off capability, 150nm increased range, shorter time to climb to flight level 450, 4-5% fuel savings, etc. Are these benefits worth the cost? That's up to the owner; but there are tangible benefits beyond aesthetics(which is a benefit to some as well).
That all sounds great in "marketing speak", but in real world operations on this airplane
And to eliminate confusion as to what they're claiming; "up to" 15 kts...which may only be achieved under certain parameters and not under all conditions. A 1,200 lb increase in MGTW (Maximum Gross Take-off Weight) which again may not always be useable depending on field length requirements. The temp increase means that the airplane will now perform at the same level in a 4*C higher ambient temp condition as it did without the winglets. When you play in the charts, it doesn't get you very much.... And a 4-5% fuel savings would take a really really really long time for most operators to have a ROI of the $415,000 winglet kit, plus the cost of installation at $178,000.
There are wing designs that the addition of winglets makes significant gains. But because of the efficient aerodynamics of the original wing design by Cessna's engineers, the X isn't one of them.
Again, from a source on the "inside" the idea of putting winglets on the X was orginally rejected because the performance gains didn't justify the costs. And because there were those internally that felt that they aesthetically detracted the the lines of the airplane. But customer feedback and the marketeers won out.