I haven't read much about carbon capture yet. From what I gather, pulling it out of the atmosphere would be extremely challenging because of the low concentration. A more efficient approach could be to capture it at the points of emission (chimneys etc) because concentration is much higher there.

However, capture requires a lot of energy - turning the CO2 back into hydrocarbons like oil requires essentially the same amount of energy that was gained by burning the fossil fuels in the first place. It would probably be trapped in some different form, but either way it would require huge amounts of carbon-free energy