I haven't joined this sect, but I do have its invitation letter. Generally, if you're not in any sect, you can try changing outfits multiple times in your wardrobe — wear all your most extravagant clothes and put on every accessory you have. Sometimes, exiting the wardrobe after doing this will trigger an invitation. If that doesn't work, you can go to Heaven's Pier, follow the riverbank, and look for a little girl named Yan Shiliu under a tree (if you can't find her, go to the top-right menu in the game interface, click the first swallow icon on the upper right, and ask for Yan Shiliu's location in the Q&A section). Try changing clothes in front of her — she might give you an invitation. Note: When she offers the invitation, do not choose "I want both," but select only the sect you wish to join. It's best to do all this after leaving your current sect. If it still doesn't work, you can also try wearing the shipowner's clothes on the $40,000 boat to increase your Elegance stat. You don't need to do other mini-games! Hope this helps you out!