Hi,
Growing a nail back from scratch can take up to a year. (at least for people) But after hearing your other information, I think if you could do 2 things to make it grow faster & more sucessfully and prevent it from happening again.
First, dont feed you animal dog food. he won't be getting all the nutrients he needs, or in the right amount. feed him pre killed mice (go to reptile convention & buy in bulk - its so cheap!) and things like roaches and fruit (mine love banana!). This will ensure that he is getting a steady, natural diet that will give him the nutrients he needs to grow that nail back.
Second, go to home depot and buy ORGANIC dirt, and replace your cypress mulch. cypress mulch is bad because if you have a boy, it can get stuck to his private parts when they emerge when he goes to the bathroom. also, its pokey & itchy. your tegu may have been digging instinctually to find softer, more decomposed dirt, and hurt his toes when there wasn't any.
Believe me, you think cypress mulch looks nice, Dirt actually looks really hot, especially under good UV lighting. its very clean looking, also easy to spot clean! Its the only thing I would ever use. (some people like to mix dirts, sands, clays, thats up to you!) It also may hold moisture better so you're not always spraying the enclosure!
Try those two things, and give it time, and he will probably grow his nail back!
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Zsa-Zsu and Corny the Corn Snake
and Monaco the Argentine B&W Tegu
and Meanie the Black Throat Monitor