Here’s a good tip I learned at this year’s Chelsea Flower Show, from the wonderful Auricula specialist nursery, W & S Lockyer:

If, after you have washed your old terracotta pots, there are still crusty deposits which are difficult to remove, try soaking the
pots overnight in a bucket of water to which you have added a couple of Steradent tablets [made for cleaning false teeth!].

Often, this is enough to get the pots really clean again.