There is another type of intercalated cell called β-intercalated cell, which is in essence a mirror image of the α-intercalated cell:
Right side shows α-intercalated cell, which secretes H+ ions to the urine while absorbing HCO3- into the interstitium in exchange for Cl-. β-intercalated cell, as it is shown in the left side, has the same co-transporters, but on the reverse side. Its luminal Cl-/HCO3- co-transporter allows secretion of HCO3- into the urine in exchange for Cl-.
In metabolic alkalosis, there's excess HCO3-. Now, if there's adequate Cl- in the urine, then it is possible to absorb that Cl- and excrete HCO3- in return. Indeed, if HCO3- excess occurred as a result of volume contraction (like you'd see in loop diuretics), then giving saline to such a patient would result Cl- to be filtered in the urine, which then can be exchanged for HCO3-. This type of metabolic alkalosis is saline responsive, and due to the kidney exchanging Cl- for HCO3-, urine Cl is < 10 mEq/L. However, metabolic alkalosis may also seen in pathologies with volume excess, such as hyperaldosteronism. In such cases, there will be excess H+ secretion (rather than increased HCO3- absorption as seen with volume contraction). H+ secretion is accompanied by passive Cl- secretion (not shown in the figure above). That is why in such cases, urine Cl- is found to be increased (>20 mEq/L).
In metabolic acidosis, you'd want increased HCO3- reabsorption.