Forty million won't go far. The Jordians are none too happy about it, place is flooded with refugees and they are a big source of instability all over the region. There are a lot of tribal links and the Syrian appear to be less despised than the Pals. Last I hard they were moving the Syrians out into camps in the desert.
Does either side have the logistical wherewithal to launch a serious military incursion on the other? I doubt it. Jordan is already creaking under the strain, and the last thing Syria needs is another heavy military commitment. This looks like the Syrians getting a bit trigger happy near the border, and the Jordanians sending them a diplomatic and high velocity 'watch what you're doing' back.