Great question! Green card holders are required to report their worldwide income to the IRS when they file taxes. One exception would be certain treaty benefits that may apply depending on what country they are from. If under the treaty the pension is not considered income that would also apply to the dependency calculation. They would need to file from 8833 with the tax return to only file US source income, if applicable.
To find our more about treaty benefits and how they may help go here:
Tax Treaty Benefits
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