I've done a little reading....I would quote websites, but I'm on mobile due to it being half three in the morning. Insomnia, amirite.
The active ingredient in Orange Guard is d limonene, which is classed as GRAS (generally regarded as safe) by the FDA. However, on reading I found quite a few sources that describe it as having 'low to moderate toxicity' - it can cause mild to moderate side effects if it comes into contact with skin or eyes (reactions can be severe here), or is ingested. It may also cause respiratory irritation. Bearing in mind this is in humans, and you can generally take it as read that if something is mildly not good for us, it's gonna be a lot worse for our feathered friends. As for the other ingredients....they refuse to publish them except for saying it's 'water based' and contains 'an emulsifier' and '94.2% inert ingredients'.....not sketchy at all.
It comes in a spray bottle, meaning you're going to get very small particles of it floating around in the air even if you're careful. Now I don't know if that's enough to be irritating or toxic to a bird, but put it this way: if I spray anything that isn't water, or water with aloe, I aerate the room thoroughly before bringing Peach into there. Her lungs are so tiny, and she's the size of a canary almost....well, you know what they were used for

I'm even careful with spraying perfume in the same room, which is close to my skin. I go outside, make myself smell nice, then come back.
Since the active ingredient can be considered irritating to humans and can cause the problems I mentioned above, I personally would be careful. Obviously the liquid itself will not come into direct contact with your bird, but the only worry I have is either with ingestion if your affected plants/surfaces are near your bird or the atomiser used to disperse it. If I had to use this product, I would aerate the room if I had an insect problem indoors (not common in a climate like England's is, but you never know) before bringing my bird in, and keep them away from any areas that the Orange Guard had been sprayed so they don't accidentally ingest any.
Bearing in mind this only is my two cents of advice, and there are many people on here with more experience with birds than I could dream of who will come to offer their (much better) advice soon. I may be totally wrong, but I like to think I err on the side of caution.