It doesn't sound like you made the tga sequence yourself. How did it originate?
Can you contact the person who originally did the animation? You might be able to get something that will work better for your purposes.
Actually the image was probably rendered wrongly - with a colored background instead of black. The closer the color to the grey midpoint, the bigger the risk it may not properly unmultiply. I'd "fix" it by importing the sequence twice - once with Alpha off, the other time with the Alpha. Then split the channels using Shift Channels, extract the Alpah as a matte and then re-combine after fixing any issues in the Alpha...
The original tga export was done with 3ds Max. I don't know the parameters that were used for creating and I know that the person is no longer with the company. I could see if they could re-render for me as the source files still exist. With the tga or tif format, 3ds Max can export 16, 24, or 32 bit, with both "Alpha Split" and "Pre-Multiplied Alpha" as options. I don't know what they used ( or should have used). The person who did the files that I'm using, rendered them on a white background (hence the white fringe when I try to use something other than white as a pre-multiplied Alpha in AE). Sounds like they should have been rendered on a medium blue-grey?
Mylenium, good advice, but you lost me at the Shift Channels part... I will look into that.
I'm wondering if it would work if I set up an action in PS6 to eliminate the background in the series of files and then bring those in as PSD files?
If they can give you an alpha split file, your problems probably would be over: it's a white-on-black rendering of the animation; shades of gray are semi-transparent. You use it as a Luma Matte for the original animation.
Or you could use Photoshop for the fix. Either way will work. As will Mylenium's suggestion.