My Israeli client is paying me directly. Does that affect my tax exposure?

Yes, significantly. If an Israeli entity bears and pays your remuneration, the income is Israeli-source under Section 4A of the Israeli Income Tax Ordinance, and the Israeli payer has a mandatory withholding obligation under Section 164. The third prong of the treaty exemption test also requires that the remuneration must not be borne by an Israeli permanent establishment or fixed base. Direct payment by an Israeli client typically fails that prong, eliminating the treaty exemption even if you are only present for a few days.