Tim is correct... Canon teleconverters will not even mount to a 70-300mm. They have a protruding front element that needs to fit inside the rear of the lens and the 70-300mm isn't large enough diameter to physically fit any of the Canon TCs (some lenses may have rear lens elements that aren't recessed enough to accomodate the Canon TCs, too).
He's also correct that any teleconverter not only changes the effective focal length, it also reduces light passing through (one stop with a 1.4X teleconverter, two stops with a 2X and three stops with a 3X).
There are some third party teleconverters that will physically fit the 70-300mm. Kenko Pro 300 1.4X and 2X DGX, and Kenko MC4 1.4X and 2X DGX, for example, will fit onto the lens okay. However, using a 1.4X to make the lens an effective 98-420mm f5.6-8 or a 2X would make the lens an effective 140-600mm f8-11. Your T3i needs f5.6 to be able to autofocus. A few Canon cameras can focus f8 lenses or f8 equivalent lens + TC combos (among current models 1DX, 5DIII, 7DII, with limited AF points). Also, there are a few f6.3 lenses that sort of fool the camera into focusing.
Speaking of which, it is possible to put a piece of tape over a couple of the electronic contacts on the teleconverter, so the camera doesn't know it's there.... In which case the camera will at least try to autofocus. Just don't expect too much... It will depend upon light conditions, subject contrast and more, but the autofocus will be more likely to struggle, hunt and fail. (If interested in trying this, do an Internet search for "Canon teleconverter tape autofocus" and you'll find websites that illustrate how to do it.)
You also could try to manually focus the lens. Just be aware that your viewfinder will be dimmed down, too. It may be possible to manual focus using Live View with Exposure Simulation to brighten the screen, but that will be slower.
However, even if you get around the issues of physically attaching the teleconverter and focusing problems, you still shouldn't expect too much. Adding optics to any lens typically costs some image quality. With a weaker 1.4X it may be just a little. There's more quality loss with a 2X. I have never seen a 3X teleconverter I'd use, there is so much loss of image quality. There are simply so many different possible combinations, it's anyone's guess what particular lens and specific teleconverter might work together acceptible. But teleconverters typically work better with primes than with zooms, too.
For example, I have both 1.4X and 2X, and mostly use them with 135/2, 300/2.8, 300/4 and 500/4 lenses. Occasionally I'll use 1.4X on a 70-200/2.8 lens (which will accept a Canon TC physically). But I won't use a 2X on that zoom because there's just too much loss of image quality. (Note: Newer versions of 70-200 and 2X teleconverter are said to work better together.)
You really might be better served by saving up toward a longer focal length lens, instead of trying to use a teleconverter with that lens. For example, Canon 100-400mm Mark II looks to be an excellent lens, though it's over $2000. The first version of the 100-400 can be found used for under $800. Sigma 120-400mm OS and 150-500mm OS are now selling for under $500 (can be found new for $800 or a little more). And there are Sigma and Tamron 150-600mm lenses selling new for $1100.
Canon 400mm f5.6 is an excellent prime for about $1250 new, or for $900 or less used. However, plan on using a tripod or at least a monopod because the 400/5.6 doesn't have image stabilization (while all the other lenses mentioned do have it). Stabilization is a very helpful feature on a very long telephoto like this.
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7D(x2), 50D(x3), some other cameras, various lenses & accessories
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