That’s the pink elephant thing. Where if someone says “don’t think of a pink elephant!” The very first thing that pops in your head is a pink elephant. It’s especially true with AI models.
You’re better off just leaving the monkey part out. Or, as someone else mentioned, use a negative prompt if possible. But Bing doesn’t have one.

You could try something like “without any animals “ where animals is too generic to trigger something like an animal to appear?

But anyway, these are so damn cute! The top one makes me think of a Bananya spin-off :)