Inquiry regarding load current

Part Number: TPS63020-Q1
Other Parts Discussed in Thread: TPS63020

I am currently using the TPS63020. 
The input power is 5.1V and the output power is 3.6V. 
The input power source is a super capacitor.
As shown in the provided waveform, the maximum current momentarily exceeds 4A during operation. 
In practice, the TPS63020 does not operate continuously, but only supplies current to the load through the TPS63020 during safety mode operation.

Could this behavior damage the product? Thank you.