Is the problem that the points extend into the seam allowance, or that the setting units/triangles are too narrow? There are different fixes.
When your star points are where they should be, but there is not enough seam allowance for them or the background you can put in gentle arcs of fabric, think like a wedding ring melon piece. With a busy printed background you won't even notice. If you have no more matching fabric you can go for a contrast/connection to a border which would mean doing all the blocks even the ones that came out ok.
And then the question is how noticeable is it really -- sometimes like on two-color quilts yes, it is really noticeable and if it is going to bother you, this is your chance to fix it. Other times, like if it is scrappy anyway and next to a busy print once you get 5 feet away those points might not be so noticeable.
I spent my first 20 years of quilting trying to be very precise both in my cutting and my piecing. These last 20 years I've been slowly moving towards the cut/sew large and trim down school of thought. When I was being precise I still would check my subunits and trim a thread here or there, now I make sure I have enough to be worth trimming! The extra 1/4-1/2" per piece doesn't add up to much, whether it is from strip piecing techniques or my single techniques. For me it is faster and ultimately more accurate and a happier process accepting that I am not using every thread but I am getting the results I want with minimal redo.