When you remove the spoiler try using a plastic putty knife to pry the clips loose. The clips do most of the holding. There will be about 6 or 8 3/8 holes which will need to be welded closed. They are too big for body filler. I know because I tried. So I sliced up some 3/8 rod and welded the small slices in place and refinished the complete gate with body filler, primer and base coat / clear coat. In addition to the holes, the paint was worn away on the corners where the spoiler contacted the body so I had to refinish the complete rear gate. You will also need a 3rd brake light from an NA 300zx because the 3rd brake light in on the TT is in the spoiler. I ordered on the spoiler from a dealer because its fragile and shipping is an issue. The Nissan box is huge. The NA 3rd brake light is large and brittle but clips and bolts right in.
You could try to repair and refinish your spoiler. My spoiler had cracks that were not visible until we primed it. When we flexed it slightly the cracks became visible. There is a product that is used to repair the polyurethane front bumper found on mid 1970 USA cars like the Corvette and Firebird. This might work on the TT spoiler. I like the clean look and stealth of the NA body so I did the work and deleted the spoiler. I sold my old spoiler with cracks on eBay for $100 this helped offset the many costs of this project.