Oggy's relatives come to visit him. Oggy believes that the cockroaches will sabotage it and make his relatives run away, because he thinks his relatives have a fear of cockroaches. Hence, Oggy makes everything act like they are not there and that he did nothing, making him almost too timid due to the cockroaches' sabotaging plan.
Oggy and the cockroaches were having a usual day, when the relatives of Oggy came to visit him. Oggy thought that they will be scared of the cockroaches and will leave, so he tried his best to make his relatives do not see or know about the cockroaches as much as possible. They came to know that and created traps for his relatives, but Oggy makes the traps beat him instead.
It's unknown what his relatives are, but the male cat looks more like in the slideshow from Love and Kisses, which could be possible that he could be his father, while the female cat looks more like she's Oggy's aunt, or she could also be his mother, just changed some years after Oggy's birth.
When Oggy is imagining his relatives' reactions to his roach problem, the female cat's eyes are purple instead of green.