Previous owner overlayed a wood deck on top of an old concrete one - do I need to fix it? Is this deck even done correctly?

House was remodeled from its original owner a few months before we bought it. Most of the work was done better than expected, but this deck has never sat right with me.

The old concrete pad is still under there. It seems to retain some amount of water underneath when it rains. The deck is also showing sun fading already (see last picture) and it hasn't even seen its' first summer yet.

They left the labels on the wood, shown in the last picture.

I know very little about decks, is this even well made? Should I just rip this out and have someone come install a real engineered fill base + Trex?