Details
It’s a little helper ingredient that helps to set the pH of a cosmetic formulation to be just right. It’s very alkaline (you know the opposite of being very acidic): a 1% solution has a pH of around 10.
It does not have the very best safety reputation but in general, you do not have to worry about it.
What is true is that if a product contains so-called N-nitrogenating agents (e.g.: preservatives like 2-Bromo-2-Nitropropane-1,3-Diol, 5-Bromo-5-Nitro- 1,3-Dioxane or sodium nitrate - so look out for things with nitro, nitra in the name) that together with TEA can form some not nice carcinogenic stuff (that is called nitrosamines). But with proper formulation that does not happen, TEA in itself is not a bad guy.
But let’s assume a bad combination of ingredients were used and the nitrosamines formed. :( Even in that case you are probably fine because as far as we know it cannot penetrate the skin.
But to be on the safe side, if you see Triethanolamine in an INCI and also something with nitra, nitro in the name of it just skip the product, that cannot hurt.