I am a foreigner living in the USA. I sometimes come across veterans and I know that in the local culture it is custom to respectfully acknowledge their service. Nothing too fancy:

Person A: "... I then joined the navy and served for 5 years."

Person B: "Oh, thank you for your service."

Would it be appropriate for foreigners to offer similar regards?

If context matters, I'm usually the more senior in the conversation (e.g. in an interviewer position).

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* I'm fairly new in the US (less than 10 years) — I guess that at some point, if I stay, the dilemma would become redundant as the thank you may come across as more sincere since I would have more to actually thank for (I would have "benefited" more from veterans service)
* I come from Israel, which I guess folks have mixed feelings about. However, I usually do not state my home country when introducing myself (as it seems irrelevant) despite my heavy Middle Eastern accent.