The first time Allah mentions this "our hearts are covered" quote is in Surah Baqarah:
And they said, "Our hearts are wrapped." But, [in fact], Allah has cursed them for their disbelief, so little is it that they believe. (2:88)
Your understanding of it is more or less correct. They are using this as an excuse that they cannot understand what the Prophet (SAW) is telling them. This is obviously a lie. They understand exactly the message of Islam. But, they refuse after understanding it.
And for this disbelief, Allah cursed them and removed them from his mercy. After this action (i.e. claiming their hearts were covered) and others like it, they are prevented from belief.
One tafsir (As-Sa'adi) for reference:
As their excuse for not believing that to which you, O Prophet, are calling them, they stated that their hearts are impenetrably wrapped. What is meant is that their hearts are covered over, so they do not understand what you say. In other words, they have an excuse - or so they say - for not understanding. But this is a lie on their part, hence Allah said: (Nay, Allah has cursed them for their disbelief) that is, they are cast away and cursed because of their disbelief and the believers among them are few, or they have little faith and it is their disbelief that is prevalent (Tafsir As-Sa'adi)
Another view is that rather than them acting dumb, they are acting arrogant. Ibn Abbas is quoted in Tafsir Al-Qurtubi:
قَالَ ابْنُ عَبَّاسٍ: أَيْ قُلُوبُنَا مُمْتَلِئَةٌ عِلْمًا لَا تَحْتَاجُ إِلَى عِلْمِ مُحَمَّدٍ ﷺ وَلَا غَيْرِهِ.
Ibn Abbas (RA) said: Meaning, our hearts are full to the brim with knowledge and need no knowledge from Muhammad (SAW) or any others.
In this view, they are saying their hearts are so wrapped in knowledge that they don't need Muhammad (SAW)'s message. And for this disbelief and arrogance, Allah curses them and makes them stay in disbelief.
