There is a file /wp-content/plugins/speakout/includes/countries.txt which contains a list of countries. This is the default country list.
If you want to have your own list, firstly make a copy of that file and place it in /wp-content/plugins/speakout/custom. If this file exists, it is used instead of the default file.
Each country must be on its own line and has a separator
| (a pipe symbol) between the English name (for the database) and the display name which can be in the language of that country.
Country names can also be listed in whatever order you choose and you can even remove all the not needed countries e.g. if your petition is limited to Mexico, you might remove all other countries to make the page smaller to load and also less complex for users.
Any files in the custom directory will remain untouched during updates, so your custom strings will be safe.