The short version is, your gear should be updated automatically, with no need to re-farm any pieces. Here is some more information:

• If an item base type is reworked, your items will retain their affixes but become a different base type. Changes to the minimum/maximum of affixes on all item types apply automatically.
• If an affix is removed, it will be replaced on your items with a different random affix.
• If an affix is removed from the affix pool of a certain item type, any existing items will still have that affix but no longer be upgradeable/craftable on the item it was removed from.