Will there be problems bringing an ointment that is labelled in grams through TSA security?

Since it's a prescription ointment, it's not subject to the 100 ml / 3.4 fluid ounces rules anyway. Have the prescription label on it and clearly readable, and make sure the name matches the name on your boarding pass and in your passport, and you're fine. (This is more than you technically need because the rules just say "medications" but why give a security officer something to argue with you about?)

(I read about a security blogger who brought two separate one-litre bottles labelled Saline Solution and with official-looking labels on them through security. According to the story when questioned why he needed two, he replied "I have two eyes" and that was good enough for them.)

In my frequent flying experience TSA never bothered to actually check the container size as long as the container looked "small enough" and otherwise didn't deserve attention. They only did that when a container was visibly large.

This is however not a case in some other countries. In Japan Narita, for example, there they will go through every single one of them, and will throw away anything over 100ml. Lost there a nice shaving cream (109 ml) which flew with me through US and Europe on like seven flights in a row.

I don't know if the TSA also has weight or mass limits but the 3.4-fluid-ounce rule is a volume limit (more-or-less equivalent to 100 ml). In any case, it would seem that the container needs to be smaller than that, by volume. A mass in grams or even in ounces does not directly indicate that.

Based on my extensive experience I would not expect you to have any trouble - as long as the number of on the label is below 100 grams.

Many years ago I found a specific brand of deodorant spray that labels all of their products as being "150ml" or "150ml/100g", with the exception of one particular product which, despite being in the exact same size container, is labeled only as "100g".

I regularly (and I mean at least weekly) travel with a can of this "100g" spray in my carry-on bags, and have traveled to over 30 countries doing do. Probably one out of ever 4-5 times the airport security staff look at the can as they presume it is over the allowed size (and in some sense of the word, they are correct) - but to date I have never not been allowed continue with it. I have had a small number of security people who have looked at the can in great detail (including all the fine print on the back) looking for a size other than the clearly-shown "100g" on the front of the can, but they always fail.

I have been told by security staff in some countries that their criteria is that any labels must show below "100ml" AND "100g". ie, "150ml/100g" is not acceptable, but the exact same size can showing only "100g" is.

Obviously your experience may vary - but based on hundreds of trips through security in dozens of countries, I'd suggest you'll be fine!

The TSA and other airport security entities are way too dumb to understand that grams and milliliters are different. Example: I tried to leave London a few weeks ago with a 125 gram jar of Marmite. Now, Marmite is an heavy edible paste with a specific gravity of at least 1.5, so 125 grams of it certainly displaces less than 100ml. There was no point in arguing this to the security doof, so I just let him take it.