Step 1: Understand what chelation therapy needs.
To pull a toxic metal like lead out of the bloodstream, doctors use a ligand that can grab the metal ion tightly from many sides at once and form a water soluble complex that the kidneys can then flush out in urine.
Step 2: Compare the denticity of each option.
Ethane-1,2-diamine and the oxalate ion are both bidentate, holding on with only two donor atoms, and dimethylglyoxime is also bidentate and is really suited to detecting nickel rather than treating poisoning. EDTA, however, is hexadentate, offering six donor atoms, two nitrogens and four oxygens, that wrap completely around the metal ion.
Step 3: See how this plays out in the body.
The calcium salt $CaNa_2EDTA$ is administered, and because $Pb^{2+}$ binds EDTA far more strongly than $Ca^{2+}$ does, the lead simply displaces the calcium: \[ [Ca(EDTA)]^{2-} + Pb^{2+} \rightarrow [Pb(EDTA)]^{2-} + Ca^{2+} \]
Step 4: State the answer.
The resulting lead complex is stable, non-toxic, and easily excreted. \[ \boxed{\text{EDTA}} \]