Under the Blood

I had recently asked a lady from Assembly of God Church, to pray with me about specific issue.
This is an older lady there who is considered in high regard.
She prayer, and she kept saying "putting this under the Blood"

Now I've been hearing people pray like that before. I just became curious about the Theology the prayer is grounded upon.
Is there theological grounds for praying in that way?

I guess for me, I would just tell Jesus the problem. I just don't see how speaking the problem 'under the blood is praying to the Lord Jesus and bringing it to Jesus.
Or thru Jesus to our Father in Heaven.

Thank you, it is helpful. Though, I am not sure who the author is. Chasing down the about page, offered me more information about authorship.

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