Consider a person A who works regular 9-5 job vs a person B who works for a company in another country remotely, does the bank see person A and person B differently at all provided that they make the same salary?
I suspect remote/on-prem would be much less important than the difference between permanent employee with predictable salary versus freelancer/contractor with less predictable income.
If the bank were really on the ball they might try to estimate the probability of you losing your income stream and the probability you'd be able to replace it with a new one to keep paying off the mortgage. Then where you lived and what local opportunities for work were available might come into it. Giving a loan to a person in a small town with only one big employer / one industry is riskier than giving a loan to someone in a location where there are many alternative opportunities for employment. But on the other hand, land is probably cheaper in the small town, so the loan might be smaller..
Based on my experience, no. They look at the documentation of your income and debts. Where I physically sit when I work simply wasn't asked.
I can't say for sure, but my take is it probably wouldn't, based on a couple things:
1. I've known people who work sales for companies located across the country. We don't consider these jobs "remote" like the tech world, but they're similar in most respects. They own a home in a different city than their employer.
2. Banks and brokers are, for the most part, dying to give away money. The employment section of the mortgage application often doesn't ask much more than how long you've worked at your employer and what your salary is (sometimes a letter from your employer is required, but should be no problem).
Just apply, it doesn't hurt.
I'm not sure they would even know / bother to check.
I've regularly worked for companies located far from where I bought a home. The topic never came up outside of income.
Feel free to ask a mortgage broker or rep from the mortgage company, they are happy to answer questions.
I had to have my manager sign a letter that I was a full time remote employee.
May be it does.