Can anyone help with the concept of deletion construct?

I don't think you're actually trying to delete the gene. By performing PCR, you're creating many copies of the upstream and downstream regions -- this is typically where the regulators and promoters are found. These regions control the expression of the gene. I'm guessing you're going to insert these segments into a vector and then into the bacteria so that they take up this new promoter. Then the expression of the gene will be regulated by the new promoter that you inserted, instead of the original one.