This is a really cool question!

Among the valuable consumer goods that a Roman could reasonably expect to find in Carthage would be the purple Tyrian dye, or the ingredients to make it. This is because Carthage was founded by Phoenicians, who brought their dye-making expertise with them. Granted, it is fairly hard to determine the prevalence of goods like dye or textiles in general at a site that is 1) thousands of years old and 2) got totally wrecked by invasion and looting multiple times over that span. But wait! We have a pretty good way of figuring out if Tyrian purple was being produced somewhere: by looking for caches of snail shells, which don't decompose! (Tyrian purple is made from snails.)

We've got a few deposits of the specific kind of snail shells that you'd expect to find from a Phoenician dye-making culture. Alas, the ones from Punic times (i.e. the time that Romans are looting the place) are small and not like the big, Costco-sized shell middens that major dye production would require. I insert my own interpretation that this simply means that the actual production of Tyrian purple was not a key priority for Carthage at this time -- presumably, they'd still be shipping the stuff in from the old country, because rich people want their dye. And the textile industry was definitely present in Carthage, given by the contents and decorations of their tombs and whatnot. (Side note: Carthage is also known for child sacrifice. If he's doing much grave-robbing here, our Roman soldier should probably stay away from the Tophet if he wants to keep his lunch.)

Tyrian purple dye, or cloth treated with the dye, would have been very valuable for the average Roman -- and portable, too! Now, it is true that the Roman government sought to regulate the use of this particular color, limiting ownership of purple togas to senators only and purple-wearing in general to specific days. However, this movement to restrict use of Tyrian purple didn't really take off until Julius Caesar, and it was not until Nero when purple was limited to the imperial family. The Punic Wars were fought by the Roman Republic, and there are no emperors in Rome! (Not yet.) Anybody who can get their hands on some of that beautiful purple would therefore be able to wear it as they saw fit, or more likely sell it to a dye merchant, cloth merchant, or really rich person to snag a quick profit.

So, go and loot some sweet clothes! Or, failing that, grab a bunch of coins, because gold is gold wherever you are, and you can spend it immediately.

---

For further reading on Carthaginian textiles, funerary rites, and stuff in general, see:

Bergeron, Marianne E. “Death, gender, and sea shells in Carthage." Pallas 86 (2001): 169-189.

For further reading on Roman sumptuary law, including regulation of the color purple, see:

Elliot, Charlene. “Purple Pasts: Color Codification in the Ancient World.” Law & Social Inquiry 33 (Winter, 2008): 173-195.

You could simply hang back and do whatever you wanted, as loot was tightly controlled by officers. They made sure everybody got their "fair" share. The General took the biggest slice, Socii Soldiers the least amount. In the end, most soldiers were happy with what they got, because it was still more than what they would have earned on their farm.