Regular Expressions can't be used with the Search and Remove Text command.
It is possible to do it with JS, but it is a complex task, especially if you want to find text that is longer than a single word. The issue is that JS can only access one word at a time from the text of a PDF, so if you try to match a whole phrase against a RegExp it becomes very complex to keep track of where the phrase is located and whether it's a match.
If you only want to find single word phrases, it's less complex (but still not trivial).
You basically scan all the words in the file, looking for matches against your regular expression, and when they are found you place a Redaction annotation on top of those words and then apply the redactions at the end.
I have developed certain such scripts in the past, for example for the removal of Social Security Numbers or Credit Card Numbers from PDF files.
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