Had one trip to the US where they asked how much money I was carrying. I said none, just a credit card. They asked if I were planning to work there. I said no, I'll pull money from the debit card as I go. They (presumably) acted puzzled about this.

The general rule is "if you make money while in a country, you need a work visa while in that country", but obviously that may be a bit outdated and not take into account remote positions. Many countries can/will fine, blacklist, and deport you if they find out you worked while within the country without a work visa; and it's _those_ people that you need to be able to convince "I'm not taking your jobs away!" to.

I'm a US citizen so I haven't looked into it from your POV, but I do know that a trip to Canada, for example, allows working remotely as long as:

* you work for an American company with no Canadian offices or branches[1],

* you are paid in American dollars, and

* that payment is deposited into an American bank account.

Again, depends on the country you're visiting (and possibly the country you're a resident of), so I'd double check before working on a trip just to be safe.

[1] If your company has branches where you're going, the safest bet is to get them to help arrange the trip. A have a family member that travels a lot on business and has been denied entry to countries while on business trips specifically to train the local branch, because even then it's a delicate situation.