Words that are derived from Arabic or Persian often use the letter ग़. Although many Hindi speakers don't make any distinction between the pronunciation of ग़ and ग, it becomes important when you want to use the original pronunciation or want to transliterate into the Nastaliq script for instance.
Is it intentional of Duolingo not to make a distinction in the pronunciation? ग़ here is pronounced just like ग, ख़ was pronounced like ख. Wouldn't it make sense pedagogically, especially when introducing new letters, to pronounce them as spelled? Otherwise we 1) don't get to hear the sound and 2) get confused.
You certainly have a point and I hope Duolingo considers it, especially because they have made the decision to go with these written forms rather than just using ग,ख etc.
That said, most Hindi speakers who are not also exposed to Urdu, will not make a pronunciation distinction between the letters with a nuqta (dot) and without it (except for ड़ and ढ़). This is less true with ज़ and फ़ which are also present in English loanwords but almost always the case with क़, ख़ and ग़. So, the TTS is more in line with the real world. In fact, it is increasingly common to drop the nuqta in writing as well (except with ड़ and ढ़ again). You will see गलत and खरगोश ('rabbit') a lot more often than the 'correct' forms ग़लत and ख़रगोश.