Well, Green water is not a bad thing for the fishies. I have had green water so thick that unless the fish were pressed against the front of the glass you could not see them. But I digress -
The green water, or pea soup, is an algae bloom. Free floating planktonic single celled algae is what is turning the water green. The cause is almost always, excess nutrients (nitrates and/or phosphates) or excessive lighting.
Algae consumes oxygen at night and a severe algae bloom can reduce oxygen to critically low levels, so while treating the tank, try to increase water circulation until you have the problem solved.
Common causes:
Overfeeding - Most aquarium flake food is high in phosphates and as the food decays these phosphates are released.
Infrequent filter changes - Decaying material in the filter can also cause increased nitrate and phosphates.
Infrequent water changes - Water changes is the method used to control nitrate and phosphate levels in your aquarium. Phosphates can also be controlled through the use of phosphate pillows available at your local aquarium store.
Excessive light - not only aquarium lighting but also might be intense room lighting like you mentioned eariler.
Solutions
The solution is twofold. First eliminate the current algae bloom and secondly prevent it's return. The only way I know to control algae blooms is to control the nutrient and lighting levels of the tank.
Getting rid of the current algae bloom
Covering the tank for 72 hours wouild do it. Read about it by clicking here
Green Water Treatment. During that time you can't allow any light source to enter the tank. Again I would recommend increasing the water circulation so as not to deplete the oxygen.
Aquarium clearing chemicals - especially the flocculents that bind tiny bits of debris into bigger, easier to filter out clumps, can be used to clarify the water in a few hours or overnight.
First to prevent return
Reduce feeding - You need to assure that all of the food is eaten
Reduce light - If indirect or sunlight look for ways to reduce (I liked your idea of foil on the outside back of the tank). Reduce the number of hours the tank lighting is on.
Increase filter changes and water changes - to control nitrate and phosphate levels.
Vacuuming the gravel will also help.