Tactless people are said to be insensitive to other people’s feelings though they don’t necessarily set out to be rude or insulting. They might be the type to blurt out something inappropriate without thinking about it first.

Your colleague might or might not be aware of this, so you have to approach this gently. Try talking to him about his remarks and if he is aware that hhe might have caused offence, advise him to think before speaking. You could also suggest that he mend things with an admission and simple apology when he says something tactless.

If he doesn’t realise his tactless behaviour, you might need to sit him down and give some examples of insensitive and harmless remarks. Encourage him to assume that everyone might be ultra-sensitive so he has to practise a bit of self-censorship.

Of course, he might get defensive or offended and this may sour your relationship with him. All in all, it’s your call whether to advise him or just ignore it.