Does it have a socket for external audio in for the FM transmitter ?
I have an el-cheapo FM car transmitter that has a line-in socket, and the socket is wired to the output of the mp3 decoder and the input of the FM transmitter chip. (So you could use it as a line out, perhaps with a bit of rewiring.)
It's hard to say. The basic problem is twofold: one, the manufacturer's description displays a poor understanding of the English language, so we have to guess what they "really" meant by it. Guessing often leads to bad results.
For example, it states:
" ... It supports a2dp function. ..."
Maybe by "a2dp" they mean 'analog to digital processor'. Or maybe not, because they follow that with " ... So you can play music on your headset with the Bluetooth function. ..."
Do they mean it will transmit from pen drive to a Bluetooth headset?
Secondly, going back to the OP, it might be useful to avoid the question completely and look at the problem itself: poor quality. Bluetooth is not likely to send good quality audio from anything to anything. 'Adequate' might be over-achieving. This brings up the question of exactly what level of quality the unit is capable of in the first place; certainly they are willing to tout an inherently poor quality option as a feature.
FM has the ability to transmit and receive good quality, but there is plenty of opportunity to do it badly as well. We don't know the performance of the D/A converter. Is it 16-bit? If so, in line with typical 16-bit consumer/computer grade D/A processors, it's probably not capable of resolving more than perhaps 12 bits.
Is it 8-bit? Possibly, certainly Bluetooth is up against it's inherent limits with an 8-bit signal, and some of the more aggressive mp3 formats easily fit into 8 bits, but nobody's going to be fooled into thinking it's high quality. So, taking a line out, if you can, from the D/A processor's analog out and soldering an output jack might not do anything as far as solving the problem goes.
If it were me, I'd burn a few mp3 CDs and be done with it. Alternately, rather than trying to get a line out, I would see if I can find the FM transmitting antenna in the unit, and add a length of wire to it. 14.25" is 1/8 wave for broadcast FM. That should significantly increase the S/N of the FM transmitted signal.