First, let me review Gore-tex implants for you.  These implants are not a filler but rather a surgical implant made by Surgiform and made from ePTFE (expanded polytetrafluoroethylene).  They are or were used for many purposes in surgery although they are not used nearly as often as they once were ,since we have far better devices now.
The implant that was typically used for lip augmentation and nasolabial folds and is not longer available as it tended to deform after time due to implant capsule contracture.
You could lay Bellafill or any other filler in the soft tissue in your smile lines around your implants but the injector noose to be very careful not to put any in the implant capsule.  I would not recommend this approach however, as it could cause issues with further deformation of the implant or an infection in the implant space.  Even if you get a good result by filling over and around the implant, the implant is prone to further shape change, like it has already undergone, and then you will be unsatisfied with your result.
My preferred treatment to get the best result would be to first remove the implant.  This can be done with local anesthesia from the buccal mucosa.  Once the area has healed, it will return to its native state or what you would look like if you had never had anything done.  This would be about 3 months after removal of the ePTFE implant.  At that point you could easily be treated with Bellafill or any other filler to get your desired NLF correction.
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