# [Red], <s>136</s> 120 bytes

    func[s][a: charset"<>"until[parse s[any[change["("t: a"<"a")"](t/1)| change["("a">"t: a")"](t/1)| skip]]2 > length? s]s]

[Try it online!][TIO-kksk0ijv]

[Red]: http://www.red-lang.org
[TIO-kksk0ijv]: https://tio.run/##ZVIxbsMwDNzzCkKTNBXtaBDXP3QVNBiJnbhNncB2hgL9u0uKsh2jHghLd7o7Uhqa0/zRnGI6tNXcPvpjHFOsKzpe6mFsJsdwj37qrvGuaxpj3f9EAftzE513U0W1Y1e74JKfXl7DL21g7WCEDRy/untKbwS6Nv15urzTmMY0t7ehqY8XGinSgeRzADv7Y/YMDmXlAYQV84IxghQOgdddD6FxEACC7vgsGIuE8H1GpWSmSqzndaFYljH/vJBzK0s8TCEHEKjQy6ac2/TUw4rGlWpMZF22JsLWk9Gt1cUYGoetsacUYrxLjeKQu9r8kWNy4eCpB9jwtBnG/9ywyCgxuYTHEwtsRJgMLHgoU8Pm5ss8y73kYrrGZ@ydeR2Ntp7/2GSx1@X1irIUlmFjGXbuYD8NVcqn9MaW3vROs7PeRop0H7p@ovh9u57kbbqqctTS0Hzeul4fuO7J206U5j8 "Red – Try It Online"

More readable:

    f: func[s][
        a: charset "<>"
    	l: [change["(" t: a "<" a ")"](t/1)]
    	r: [change["(" a ">" t: a ")"](t/1)]
    	until [
    	    parse s[any [l | r | skip]]	
    	    single? s    
    	]
    	s
    ]