complex shape join and trim

Hello,

In the elevation shown below, each navy blue/black star represents a piece that is sitting above some lace-like trim (shown in red). I need to trim out the red lines that go inside the shape of the star using grasshopper.

In addition to this, the stars are split in a few pieces. (as seen in the second image) I tried joining the curves, however, the tolerance between the small splits is giving me difficulty.

How can I join the outline of the individual stars efficiently through grasshopper and trim out the red lines through grasshopper?

I greatly appreciate any input or advice! I have attached more photos and the file with the lines.

Thanks,

J