I didn't doubt, that you have seen the ripple in a measurement, but if it really represents a current of 3.3 A. I understood, that a
switching power supply would be involved in the circuit, that causes the ripple. If this isn't the case, only an oscillation either on the
load or the source side can explain the ripple. But can it create a high current amplitude? The LDO input current e.g. is uni-directional.
With 200 mA load, it won't generate more than 400 mA pk-to-peak at worst case. But you didn't tell about other circuit parts connected
to the capacitor.