She told the story to Jagya to highlight Akheraj's atrocities and not because she thought he would help her find the child's mother.
Once the story came out there is nothing she could do because Jagya already guessed that N is Anandi's daughter and he wanted some proofs to show Anandi.When J saw the locket there was no way she could stop the child going to her mother.
She lied to the child about the clothes because they did not go with the garbage dump story.This was long before Akheraj was exposed.
She stuck to the garbage dump story from the begininng when it came to that child. She told the truth to Chagini and Jagya but why didn't she tell the child?Because it suited her purposes.
The child believes the garbage dump story because Mangala also went along with it.If it had been only Harki and Akheraj who said that she was found in garbage dump she wouldn't have believed that story because that child knew what kind of people Harki and Akheraj are.
The lady shined brightly only because of Akheraj and Harki and she wasn't cruel and callous like them but now she outshined Harki and Akheraj when it came to cruelty and callousness.
What's more it is to create sympathy for the child and not for Anandi.
The child is always seen as Anandi's estranged daughter regardless of the fact whether she was called Nimboli or Nandini.
It is quite clear now they want to establish the child's character on it's own independent of Anandi so they created this OTT drama to make the child upset enough to run away.
Anandi's child won't run away from home but Mangala's child can run away.
Anandi's child was snatched from her and the child whom Mangala calls her beti has run away.😛