Silver metal is showing at gumline on completion of my tooth implants. Can this be corrected without removing implants? (Photo)

If this portion of the bridge does not show when you're speaking and smiling (without lifting up your lip with your fingers), then it may not be an issue that needs to be addressed.The metal is either showing because part of the implant is exposed, which is unlikely, or because The bridge simply wasn't made to sit close enough to the gumline.The clicking that you describe could be caused by a screw that sits underneath the bridge that needs to be tightened or the cement on the bridge is loosening up.I hope you found this information to be helpful,Dr. Champagne

Hi:The click sound is definitely a concern.  This could be due to loose abutment and must be verified by clinical exam and xray.  If the bridge is completed seated and the neck of the implant is showing, most likely it can not be covered.  Please contact your dentist and voice your concerns right away.Best,Dr. Maddahi

It is a little difficult to make out the area you are showing in the picture but it does appear to be an area where the bone width may have been limited. If you had that tooth missing for a long time prior to the implant placement it is common to see the bone width decrease rapidly. 
If there was bone there prior to the implant, and the metal did not show previously then I would suggest you contact your dentist regarding your concerns. As mentioned above the click is a concern and should be evaluated also.
As far as your question regarding correcting the situation without removing the implant. To answer that there has to be a lot more information regarding the situation. photos, radiographs (Xray Film), CBCT (3 D image) 
If its an aesthetic issue but there are no other problems then further treatment will be up to you. If the metal exposure is due to loss of bone around the implant and progresses then you may have to consider further treatment in the future.
you should be able to talk with your dentist about your concerns and get an idea of why the situation exists and what can be done about it.