Using removeComments from commandLineParser. This is more robust as it removes both single and multiline comments

src/compiler/commandLineParser.ts

@@ -503,7 +503,7 @@ namespace ts {
      *
      * This method replace comment content by whitespace rather than completely remove them to keep positions in json parsing error reporting accurate.
      */
-    function removeComments(jsonText: string): string {
+    export function removeComments(jsonText: string): string {
         let output = "";
         const scanner = createScanner(ScriptTarget.ES5, /* skipTrivia */ false, LanguageVariant.Standard, jsonText);
         let token: SyntaxKind;

src/services/jsTyping.ts

@@ -21,8 +21,7 @@ namespace ts.JsTyping {
     function tryParseJson(jsonPath: string, host: TypingResolutionHost): any {
         if (host.fileExists(jsonPath)) {
             try {
-                // Strip out single-line comments
-                const contents = host.readFile(jsonPath).replace(/^\s*\/\/(.*)$/gm, "");
+                const contents = removeComments(host.readFile(jsonPath));
                 return JSON.parse(contents);
             }
             catch (e) { }