In short: find a storylet that consumes your Fascinating quality. There should be something in Veilgarden involving the Struggling Artist, the Artist's Model, the Honey-sipping Heiress, or the Honey-sipping Jewel Thief that requires Fascinating; if you don't have enough Fascinating to play one of those storylets, build up your Fascinating further until you can.
In long: Fascinating is a "progress" quality, so the usual sequence is that you build it up to some level, then cash it in at a storylet that requires it. So you might build up your Fascinating up to 5, which will allow you to play a storylet that a) requires at least Fascinating 5, and b) whose success is based on how high your Fascinating is. If you like, you can spend extra actions increasing your Fascinating higher so that you have a better chance at success, because failure will usually decrease your Fascinating quality. (I don't recommend it, though; the extra actions you'd spend building up your Fascinating to increase the odds of success are better spent by simply taking the plunge, and spending a few actions to build up your Fascinating again if you fail.)
There is no way to simply dump your current Fascinating if you don't qualify for any Fascinating-related storylets. So if you're at some low level of Fascinating and can't cash it in right now, the only way to reduce your Fascinating is to build it up higher so you qualify for a storylet where you can cash it in.
If you've somehow managed to hit a sweet spot in your Persuasive quality where you can't build up your Fascinating, can't dump your Fascinating, and still want to get to Fascinating 0, there is an option: buy a Talkative Rattus Faber, from Nassos Zoologicals (in the Bazaar tab). That will give you -25 to all qualities while you have it equipped, so you can re-qualify for earlier storylets (and unequip it when you're done). When you're qualifying for storylets, you always use your current quality level, including the effects of equipment and pets.
Of random interest: You will eventually raise your Persuasive high enough that you no longer qualify for the Struggling Artist and Artist's Model stories. There are other stories that involve Fascinating: affairs at the Empress' Court, investigating a Tattooed Courier, and persuading clothes to cooperate on Polythreme. Did I mention that Polythreme is a bit weird?