You make the false assumption that they only buy from us --- which is incorrect. The money sent by Mexicans working here filters up to the elite class which then vacations in Europe or somewhere else --- the money doesn't come back. The Mexican market places now import junk from China. Not long ago Mexico had a trade deficit with us --- but now we have a large and growing trade deficit with them.
If they use the dollars to buy stuff from China or Europe, they have to exchange the dollars into Yuan or Euros. That puts downward preassure on the dollar in the FX markets, which ultimatley results in inflation here.
The only way newly printed money going to Mexico wouldn't cause inflation here would be if Mexico's economy were totally closed and they were using dollars as a subsitute for Pesos. Of course, Mexico's economy is no closed.