No problem, glad you got it fixed. I blew off both of my spares before I figured out that I had a more serious issue.
You can order replacements from Amazon you need 4mm inside diameter for the tube.
https://smile.amazon.com/dp/B07P7GJCGF/ref=cm_sw_r_cp_apa_fabc_c7GaGb1W37GYR?psc=1
This is what I have here in front of me. I bought it from a homebrew supply store and I don't have the manufacturer name. I was going to just get these off Amazon to use instead of the plastic ferrule, but then I got to thinking about whether the angles of the contact surfaces would be the same/compatible (the cone angle where the seal is made). You think I'm good?
Heck, I might just try it and see what happens. It's my own home project and nothing pressing.
They're usually intended to be one-time compression fittings so unless it's been improperly assembled, it's probably not reusable. They're reasonably cheap though, check your local home improvement stores or Amazon. Worth noting, on newer versions of the Mini, they've replaced that connection with a standard pneumatic fitting - might be a good time to switch.
You sure it is not male on the Air Injection Iron Eater Filter valve? Male connection on the valve side is what is shown in the manual you posted.
And I see now they want the ferrule compression fitting to attach directly to a 3/8" male threaded tubing connection on the Iron Out and not go to 3/8" NPT. Not very common in 3/8" (much more common in 1/4" as that is the setup for an ice maker).
If you verify the connection is male on the Iron Out valve, you'll want to get a ferrule tube to insert into the end of a plain end 3/8" tube, a 3/8" female ferrule nut, and a 3/8" ferrule sleeve. Harder to find in small qty's on Amazon, but here is the smallest quantity I can find of a complete kit.
https://www.amazon.com/LTWFITTING-Compression-Insert-Sleeve-Ferrule/dp/B07FD18R9S
The copper colored bit is called a nut and ferrule and sleeve like the one pictured here: https://www.amazon.com/LTWFITTING-Compression-Insert-Sleeve-Ferrule/dp/B07FD4447K/ref=pd_sbs_469_1/132-8176869-1899529?_encoding=UTF8&pd_rd_i=B07FD4447K&pd_rd_r=26eff221-7de0-4a86-baf6-dc836235138a&pd_rd_w=nlvYM&pd_rd_wg=XUEze&...
It appears to have been crossthreaded
I found this little multipack on Amazon: http://www.amazon.com/gp/product/B00ORO4P2E?psc=1&redirect=true&ref_=ox_sc_act_title_1&smid=A12YM1PYCMRIKV- I'll be ordering those soon for modding my i3v to add a print cooling fan.