There might be a very slight benefit to removing the carpet prior to the fumigation as it is a little easier for the gas to reach the wood from above. You can ask the fumigation company to confirm.
More likely that the flooring company with include removing the carpet in their bid to install new carpets. That will probably be the easiest and least expensive way to do it. In this case, you will probably want to complete the fumigation prior to installing the new flooring.
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