i was denied access into mexico after going there many imes.this time around

the alert is due to a conviction that put me on the sex offender list, I am a tier 1 and never went to jail I did 5 years probation rom 2005-2010.I bought a property in mexico last year when I was allowed access.can this be rectified.the immigration offivcer told me if I had a letter from the embassy and my resolution papers that should suffice but I want to be certain because I don't want to be turned away again at the airport.It was dreadful my wife and friends were all there for vacation.