Footage from the incident at Carats Café in Southwick on Saturday (12 June) had been shared widely on social media.
Sussex Police said the investigation was progressing with the assistance of colleagues at Bedfordshire Police.
The same two individuals were also involved in an incident in Madeira Drive, Brighton, whereby police responded to a welfare call in respect of two dogs locked in a car, according to police.
The dogs were subsequently released from the car by police.
Superintendent Rachel Swinney said: “The behaviour of the individuals concerned in both of these incidents will not be tolerated.
"I want to send a clear message to those visiting our county that we will actively pursue those who commit crime in Sussex.”