There are three known mechanisms for this reaction. The bacterial GS-ATase (GlnE) encodes a bipartite protein with separate N-terminal AMPylation and C-terminal de-AMPylation domains whose activity is regulated by PII and associated posttranslational modifications. De-AMPylation of its substrate AMPylated glutamine synthetase proceeds by a phosphorolytic reaction between the adenyl-tyrosine of GS and orthophosphate, leading to the formation of ADP and unmodified glutamine synthetase.

Reference
Wiki: Deampylation

    Adenylylation, more commonly known as AMPylation, is a process in which an adenosine monophosphate (AMP) molecule is covalently attached to the amino acid side chain of a protein. This covalent addition of AMP to a hydroxyl side chain of the protein is a post-translational modification. Adenylylation involves a phosphodiester bond between a hydroxyl group of the molecule undergoing adenylylation, and the phosphate group of the adenosine monophosphate nucleotide (i.e. adenylic acid). Enzymes that are capable of catalyzing this process are called AMPylators.

Reference
Wiki: Ampylation