If you're concerned about people thinking that it's already the second time you call them, there's really nothing to worry about! If it's been a few months, 99% of them have already forgotten you. And keep in mind that if YOU are telemarketing these prospects, most likely others are telemarketing the same prospects as well and therefore they receive many calls.
It's just how telemarketing works: call again.
The big thing you need to consider before doing this is to be "rude" and look from the perspective of whoever you are calling, have you added whatever they are interested in and could not offer the last time you called? The answer to this question is the answer if they are likely to be interested this time - or if you should find someone else to use your time to call.
Also (at least in Sweden) it is important to keep track of anyone that explicatively said they don't wish to get contacted by you ever again if you are talking of phone calls (as that is part of the marketing laws).
If they are not interested the first time that you called them, it might be because you caught them at a bad time. To speak or to deal with someone at their inconvenient time is quite impossible. So there is still a big possibility to turn your second call into a lead.
You might also consider social media or inbound marketing to attract qualified customers. You should also incorporate a call to action or encourage them to call your business and purchase without forcing them.
I would suggest only to re-call if they mentioned during your first call that there was an interest in the new feature you just built. If they did not express an interest, I would not recommend re-calling them. Therefore, you have to take good notes with each cold call you make to determine why they were not interested and what they initially thought. You should also consider inbound marketing because sometimes it can be more effective.
Call back. Things might be changed, new people maybe leading the company, needs might change etc.