Such claims are part of the oft-refuted mercantilist view of international trade. Specifically, the claim that a nation is better off by exporting more than it imports. Whatever policies the state can impose that favor exports and discourage imports is justified. One such policy is for the state to make its currency cheaper in foreign exchange markets than dictated by its domestic purchasing power. Doing so stimulates exports by making domestic prices lower for foreigners who can trade their foreign currency for more of the domestic currency. This is what is meant by currency manipulation in international trade.
A state could use monetary inflation to manipulate its currency or it could use monetary inflation for other purposes. Monetary inflation stimulates exports only if it devalues the domestic currency against foreign exchange before it pushes domestic prices up. Usually this does happen because foreign exchange traders react more quickly to monetary inflation than the average domestic consumer. There are other ways besides monetary inflation to manipulate currencies. For example, a state could peg its domestic currency to a foreign currency at an artificially low level and then use tax revenues to supply more of its domestic currency in foreign exchange markets to keep its exchange rate at the peg. Of course, it’s more likely a state would print the additional money it wants to supply against foreign exchange. This is what China is accused of doing.
In addition to the reduced demand for Iranian Rial in foreign exchange markets, another way that sanctions push up prices in Iran is that they reduce the stock of goods Iranians have available to buy.
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