The rectangular cap on the tiller should prise off. You can either buy an new tiller extension, or repair the extension with a bit from chandler, or maybe even the chandler will fit the repair part (intact rubber doofah) for you.
How about one of these
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The problem with those I find is that they have a habit of locking during a tack as you switch sides. Not necessarily a problem in a big boat but on a tippy dinghy it can often lead to a swim!