Is there a way to get better cubs from the giving tree?

I understand that the tree collects abandoned cubs but is the object you tempt the cub with determining the cub you get?

If so, what’s the better objects to tempt with?

I know you won’t get muties since no one abandons them but when I tempt them I always end up with the same type of cub, a colourbomb or a heavily striped baby