This is the 5842nd most frequent Japanese word.
びだんごを
The word "びだんごを" does not appear to be a standard Japanese word or phrase.
In this context, 'びだんごを' refers to a Japanese dumpling described as 'green' and being the object of the verb 'もらった' (received).
彼はおばあさんから緑色のびだんごをもらった。
He received a green Japanese dumpling from the old woman.
Here, 'びだんごを' is the object found on the menu described as 'colorful.'
店のメニューには色とりどりのびだんごを見つけた。
I found colorful Japanese dumplings on the restaurant's menu.
The usage of 'びだんごを' denotes the 'Japanese dumplings' being actively created by the children during play.