Assuming that a Brita filter uses polystyrene sulfonate for its ion exchange action, there should not be an addition of chloride ions to the water. The mechanism is that sodium ions that are stuck to the polystyrene sulfonate are released into the water and that calcium and magnesium ions from the water are replaced by them in the polystyrene sulfonate matrix. At some point, all the sodium will be 'used up' and the filter needs to be replaced or revitalized by passing salt water through it to replace the calcium/magnesium back with sodium.
Ideally an ion exchange water treatment filter should not impart any chloride to the water, so my earlier remark that this may have been the problem causing the blue/yellow shift may not have been accurate. In any case, a filter using resin beads under normal operation should not impart chloride ions to the filtered water. I can very well imagine, however, that a brand new filter or a filter that has just been regenerated may contain some excess salt that ends up in the very first batch of water that is passed through the filter. This should however be quite minimal.