Why not change the area into a raised bed with new dirt?

Sounds like a great place for a Mediterranean garden. Rosemary likes dry soil, and lavender cotton (santolina), and there are flowers that actually flower better in poor soil, like cosmos. Or, you could make a gravel courtyard with potted plants.

Sounds like the previous tenant did this on purpose, since the plastic is below the pebbles. Any indication of what kind of a garden that person had in mind? Were there any plants there when you moved in?

Well start off with trying to break up the top soil using a rototiller (you can rent one). And rototill in new top soil with plenty of compost and composted manure. When amended do try planting drought resistant plants such as what Twinkle has suggested. Or you can enjoy a xeriscape or cacti garden.

By the way, you can eliminate most of the small pebbles by screening the soil away.