If your probing is accurate ( e.g. no probe ground inductance effects above 10MHz or ground shift )
Examine the ripple closely for AC and DC content. If there is no positive spike, it would appear to be resonant free. In your case the ripple is -20mV mostly at 16kHz but also +10mV component perhaps near 1 MHz.
Reducing Ripple can be a simple matter of Ohm's law or knowing the impedance of source and loads and estimating the additional attenuation required.
An active regulator with feedback offers a near zero impedance at DC which rises as feedback frequency response decreases. A series switch introduces an ESR ( perhaps from RdsOn).
In general if you wish to attenuate ripple, what impedance ratio do you have between source and load. Is there a switched capacitance load? That is your soruce impedance?
I use a nomograph for quick lookup of impedance vs Capacitance and determine both load pulse current and source ESR.
at 16kHz, 100uF is ~ 100mΩ. so if step pulse current is 100mA, it would cause 10mV spike.
Does ripple come from Capacitance, regulator frequency response? or ESR for unknown load current? If unknown you can test it with a known Capacitor of known ESR and pulse charge it momentarily and capture a 1 shot event, or, design it by known values or measure current with a small shunt i.e. 10~100 mV.