Change Lookup Group for field in List

I figured it out.

I needed to change the schema xml of the field and change the UserSelectionScope value to the ID of the created group and then update the field and the list.

string schemaXml = ownerField.SchemaXml;

//Regular Expression to replace UserSelectionScope

Regex.Replace(schemaXml, Expression);

ownerField.SchemaXml = updatedSchemaXml;

ownerField.Update();

agendaList.Update();