No "claim" is required to remove them ... the FairTax is border-adjustable taxation as is the VAT currently used by Euro (and other) countries.
This would cause problems for the VAT countries if we go to the FairTax since that would be the only tax here, but the VAT countries typically have (in addition to the VAT) corporate and/or personal income taxes which work to embed some costs into their exports thereby making them les price-competitive.
Since I (and other economists) do not believe income taxes are worked into prices I do not accept that conclusion.