As someone who travels al lot - if your employer is covering your expenses (e.g. hotel, travel costs, meals) they presumably have a policy or standard. So either they determine what hotels you can stay at or they give you a max spend. Likewise they might cover €xx per day against meals. In these cases, you will probably need receipts to justify any of these expenses (either you have a company credit card to use or you pay for them and claim them back).
Anything like that will have no effect for tax - travel expenses following a policy such as above are not treated as income.
In the past (and most often for domestic travel) some companies paid a flat rate allowance to travelling employees and it was up to them to do with it as they wished (a "per diem"). So if you could get a cheaper B&B or whatever you could pocket the difference. I think this was the idea behind the civil service allowance. I don't know of any company that operates this way anymore
Maybe, if a company doesn't cover living expenses when travelling, there is an ability to claim a tax allowance - is that the reference?