I’m going to focus on losing weight for health reasons and will be running a calorie deficit for a few months.
My goal with training was simply to be calorie neutral - replace what I use then run a deficit for the rest of the day.
When looking at TR workouts they list energy expenditure as kj(cal) ie both metrics.
My question is, if a workout is listed as 500 kj(cal) am I looking to replace 500 kilojoules or 500 calories?
Someone more knowledgeable will step in with actual facts, but IIRC I think the answer is they’re both about the same.
You pushed 500kJ into the pedals, which is equivalent to 500kcal of food.
If you do a straight conversion between the two units, you’ll find the ratio is actually about 4:1, however your body is only about 25% efficient at converting food energy to cycling energy expenditure, so it cancels out.
(But since you’re talking about input (eating), it’s kcal you want!)
Just use kj because of what Downhiller explained. When I wanted to lose about 10KG I worked with a daily deficit of 500kcal. Base rate is about 2000Kcal for me so on of days I would aim for about 1500. On days that I trained i would just add that to how much I could eat.
Great thing about that is you can still eat a ton while losing weight 
The answer, it sort of depends. I’m 21-22% efficient at 250 watts (measured in a lab), so in general I would burn a bit more than 500 kCal doing 500 kJ worth of work. For shorter rides like 1 hour, it probably doesn’t matter that much, but for a 5 hour ride you might be off enough that it matters.
I add half the calories burned back. When I’ve added them all back, I’ve lost weight at an excruciatingly slow rate or not at all. I’ve also lost weight pretty effectively counting calories while not training. Something about training and fueling seems to mess up the process for me.
I have theories:
if you do a low intensity ride, you burn a lot of fat. Maybe there is no reason to consciously replace those calories. If you were doing a higher intensity workout, then it’s probably more imperative to carb up and refill muscle glycogen stores.
Herman Pontzer who has done metabolic studies on the Hadza tribe has a theory that we tend to only burn so many calories per day. if we do manual work (exercise) our bodies slow down other processes to save energy. Thus if you replace all the KJs burned, and your body slows down other stuff, then you may not lose any weight.
Some extra info in this thread.