Not sure what the underlined text means...?

[pmda]

At in regia magnificum convivium aparatur: triclinium splendide ornatur, veste picta purpuraque Tyria sternuntur lecti, mensae vasis argenteis atque aureis teguntur.

...from Cap XXXIX LLPSI.

But in the palace a magnificent feast appeared: the triclinium adorned splendidly, the seats covered with a purple depicted Tyrian cloth....

All the underlined text seems to be ablative and is describing the manner in which the seats were adorned...

Is it a purple depicted Tyrian cloth...?

[Qimmik]

You're basically right.

picta from pingo has a range of meanings including "adorned," "decorated," "dyed," "colored," "painted."
purpura is a noun meaning (among other things) purple cloth

We might translate "veste" using a plural.

"the couches are strewn with colored vestments and Tyrian purple cloth"

In antiquity, formal dinners were eaten reclining on couches, not sitting in chairs.

Tyrian, or Phoenician, purple dye, which was made by cooking certain kinds of shellfish found in the Mediterranean on the coast of Phoenicia, was a luxury item. "Tyrian purple" reminds us of Dido's (and Carthage's) Phoenician origins.

[pmda]

Quimmik, gratias tibi ago.

Paulus