Removal is probably not called for in this situation. Spider web cracking usually is an indication of crazing, a form of plastic shrinkage cracking. Crazing generally occurs when the combination of temperature and humidity creates a rate of evaporation at the surface of the concrete that is higher than the rate of bleed water exiting the concrete. Because the surface has very little, if any, tensile strength at this time, crazing cracks start to form. The good news is that crazing is an aesthetic problem. It affects only the very top surface and does not extend deeply into the concrete. Crazing cracks are more apparent when the surface is damp.
To avoid or limit crazing, be conscious of the weather conditions during placement. If there will be high temperature, low humidity, and moderate to high winds, measures such as fogging and/or erection of windbreaks may be required during placement. Synthetic fibers will help inhibit the formation of crazing cracks. Curing must begin as soon as possible, especially in these conditions.