There is a workaround at SOLVED: How do I get a DoubleQuote in a session relevance result using the rest api that may be useful. Solution from @brolly33 in fact 
It seems to be an effect of going through multiple levels of encoding – both URL-encoding and Relevance encoding; depending on your REST client you may have the tool itself perform some url-encoding for you, such as the --data-urlencode option on Curl.
From @brolly33’s posting (which will not ‘quote’ properly here, because…some of it gets percent-encoded ). Note the use of %252522. URL-decoding represents that as %2522 and then Relevance decoding represents as %22, the " symbol.
Because of the decoding happening in multiple steps, you need to percent encode the percent to get around this.
session relevance
"%22"
rest query
https://brollytest:52311/api/query?relevance=(%22%252522%22)
on the first decode pass,
the outer %22 turns into "
the outer %25 turns into %
Then on the second decode pass you effectively have "%2522" which converts to a "%22" and finally to a """