An issue in Exporting 2D contour plot as .PDF file

Question

I have a contour plot (Windows-10, Mathematica 12.3)

For example;

 p = ContourPlot[
  Evaluate[Re[
    Product[x + I y - (a + I b), {a, -2, 2}, {b, -2, 2}]]], {x, -3, 
   3}, {y, -3, 3}, ColorFunction -> Hue]
Export["exampleplot.pdf", p]

When I zoom in on the plot, it looks like there are (six-pointed) star shapes on some lines. (Please see the following figure.)

I think this makes the shape look worse. How to get rid of them?

P.S. I want to export the plot as high-quality figures in the format .pdf or .eps. I don't want to export as .png or .jpeg or to Antialiased it.