Full disclosure: I work as a product manager for Phonak, specifically Roger at Work products.
I’m new to this forum, so hi everyone!
When it comes to products like this it is really important to really try them out for yourself. Everyone’s hearing situation is different, and what works wonders for one person might be unbearable for someone else. Ask for a trial period if possible. If you get the products reimbursed a trial period is often mandatory, though this differs between markets and countries.
Regarding things on the table: While it’s always best to have a clear path between the sound source and the microphone if possible, that does not mean that the product will not give you any benefit just because there is e.g. a glass or salt shaker in front of it.
The principle behind remote microphones, such as Roger, is quite simple; it’s all about improving the signal-to-noise ratio (SNR), i.e. the difference in level between the sound you want to hear (speech) the sound you don’t want to hear (noise). The closer you can place a microphone to the sound source (most often the mouth of the person talking) the better the SNR, as the speech will be progressively louder relative to the surrounding noise. As a rule of thumb, each halving of the distance to the sound source increases the SNR by 6dB. So if you are sitting 6ft (1.8m) away from someone and place a mic at 3ft (0.9m) the speech that reaches the remote mic will 6dB louder than the speech that reaches you directly. Directional microphone technology and noise reduction will improve the SNR further, but a large chunk of the work can be done by simply reducing the distance. As long as the object obstructing the audio path doesn’t attenuate the speech more than what you gain from the reduced distance plus any algorithms, you will still benefit from the remote mic.
If you find it’s enough of a problem you could try simply moving the microphone to a better spot or e.g. placing it on top of an upside down drinking glass to raise it up a bit in order to get a clear path.