I've had tendonitis and was able to get around it. At some point if it doesn't go away you have to take a break, IMO. Do nothing for up to a month, let it get better. Of course you'll be thinking you're losing a lot, but a few weeks after resuming training with more energy thanks to the break, it won't make any difference.
The break in training will most important get you back to normal, and secondly if the pain starts returning, should help you determine where it's coming from.
Once healed and back into training, you'll have to change the routine slightly. First of all, the warmups have to be as good as possible, which takes time. Ideally 3-4 minutes of stationary bike, nothing too intense and don't use high resistance, you just want to get the blood flowing.
Then with the weights after some thorough warmup sets you want to keep the reps higher say 10-15, on any of the exercises that have caused the knee problems. Even go to 15-20 reps per set, if that's what's needed to avoided knee strain. And at the same time, keep the rests between sets to a minute. Between those two things there will be less knee stress AND the area will be kept warm.
As a last resort if none of this helps and the pain starts returning, find out which are the problem exercise(s) and discontinue them. Either use other versions that don't hurt, or find good substitutes. For example, while standard squats are great they can be replaced with good substitutes. If pain starts returning, through the process of elimination find out what's causing it by only doing certain exercises for a few workouts each, to isolate where the pain's coming from.