) The red articles are not correct. The only grammar problem I see is " that to please look after" I would write, "A gentle reminder to all employees: Please look after personal and company assets when travelling on company business, or when at client sites. [The] company insurance doesn't cover all losses, especially during business travel.
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Grammar Geek
Simply, "travel" is not countable as you have used it.
Travel is a rather tricky word. It does not take the indefinite article (a/an) but it can be used in the plural. John Steinbeck wrote a book entitled Travels With Charley. Also, there is another book called Gulliver's Travels.
CB