IPR gap still there after refinement period. Any suggestions? (photos)

Interproximal Enamel Reduction (IPR) is sometimes necessary to create enough space for correction of rotated teeth. Basically, if you're trying to "parallel park" a car, the space has to be big enough. Sometimes you can get the other cars to move, sometimes you have to make the car a bit smaller. However, there are limitations to how much IPR that can be done before the shapes of the teeth are affected and enamel is thinned to the extent where increased risk of sensitivity and cavities are a concern. Ideally, when IPR is done, the contacts of the teeth should be approximately the same shape they were before - in this scenario, mostly flat where the teeth come together and rounding off from there. It appears that one side of the contact is flat, and the other is rounded. When those two shapes come together, it won't look quite right, even if the space is technically closed (teeth touching). At the same time, it is not always possible to achieve ideal contact shapes in certain cases (prior trauma, uneven tooth wear prior to treatment, etc). Ultimately, your dentist and orthodontist will want to make sure you are satisfied with your treatment results. Be sure to bring up your concerns at your next visit so they can come up with a solution for you. 

You should discuss with your Invisalign provider, and tell him of your dissatisfaction with the current result.  He should be able to provide additional aligners to correct this problem.  Your lateral incisor appears to be long and narrow,maybe due to overzealous IPR.   Another quick fix option would be to have some cosmetic bonding, as this is often done after Invisalign or Orthodontics to finalize a case.  There may be a small fee, but your Invisalign provider(orthodontist or general dentist) may be willing to do this for you for free to complete the case to your satisfaction.  There is a new system called EasySmile Veneers which was developed by Dr. Harvey Silverman, a cosmetic dentist from the Cleveland area.  It is based on an advanced resin technology that allows for a strong and stain resistant, natural looking veneer to be created in 1 short 15 minute visit without any filing down of your tooth, so you get to keep all of your natural healty tooth structure.  He developed this system to correct flaws in 1 or two teeth in person's smile, and this could be an ideal way to finish your case.  The space would be closed and your tooth would look completely natural.  An EasySmile dentist can create a Preview Veneer so you can see if you like the result before proceeding with the treatment.  If I had done your Invisalign, I would offer this service to you for free, if you preferred this to  wearing additional aligners.  You local dentist can receive training from Dr. Silverman via a webinar if he would like to be able to offer this treatment. You can google Dr. Harvey Silverman or EasySmile Veneers to learn more about this new cosmetic system.  

I hope that your case was performed by an orthodontist, rather then a regular dentist. In any event, return to whomever did your work, voice your dissatisfaction and ask him to request additional aligners. Don't stop until all spaces are completely closed