It will depend upon your home passport more than your greencard and travel document. The US documentation means you can get back into the USA OK, but Mexico's decision is based on your citizenship.
Here is their policy from their web site: While it is less than clear, if you are not a citizen of one of the listed countries (and I would guess you are not, since there are no refugees from these mostly western countries) then I would apply for a visa. If you don't need one, then it won't hurt.
Requirements for Tourists
Holders of a American, Australian, Canadian, British/EU Member Country*, New Zealand, Israeli passports do not need a visa to visit Mexico. They may, instead, use a visitor's permit known as an FMT.
Holders of other passports (including holders of passports of one of the 10 New EU Member Countries*) should check with their local Mexican Consulate for details of visa requirements.
For participating countries (see first paragraph above) in place of a visa, a Mexican Visitor's Permit (known as a FMT) will need to be filled out. This is a simple form: pick one up from the check-in counter at the airport and fill it out on the airplane before you land. If the airline you are traveling with does not have any Mexican Tourist Permits at the check-in desk on or board the plane, don't worry, you can get one when you land in Mexico and fill it out before you line up to have your documents checked and stamped by the officials at the airport.
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