The generally held view of traditional scholarship is that its meaning is not known to us. But why didn't the Arabs raise any objection when the verses were recited?
Your question is valid. As you know, Quran has been revealed to Prophet Muhammad PBUH in Arabic in Saudi Arabia (Arabic State). They are the people of that language who took great pride in being Arabic. There were many poets, writers, and linguists who used to compete with one another. Matter of fact, Huroof Muqatta'at have their own meanings which were used in great meaning and significance. Arabs, during that time, were knowing their meanings. I'm not sure about other Huroof Muqatta'at, but 'TaHa' means 'My Dear' or 'Dearest One' which is a Chapter in Quran.
Quran challenged those Arabs to bring some example like these, in a form of a chapter, or verse, or a word (at least) to compete with the Highest standard of Arabic used in the Quran. Later, when the non-Arabs were becoming Muslims and learning the Language, they needed to know the depth of grammar and use of the language in order to understand the meaning of each verse in its true sense. The people of Arab that time understood the meaning as and when the verses were revealed. The grammar part came later which was meant to help non-Arabic speakers learn the language easily and understand the message of the Quran.
For Huroof Muqatta'at, there are few books in Arabic that explain their meaning. When you read them, you'll learn their meaning as well. These Huroof become the top standard of Arabic which was unbeatable and to make it clear that it is coming from Allah SWT, not from any human being.
I guess it has not been published in English or any other language, which raises confusion.
Please seek the help of Islamic Scholars, hope they'll offer you a satisfying answer.