Goalkeeper Thomas and defender Stephenson have both been offered one-year deals, while striker Ings who has spent much of this season injured has been given an initial three-month offer.
The trio were yesterday given the opportunity to join Howe's first-team squad, while fellow second years Tom Hill, Tom Green, Brad Magookin, Matt Kemble, Matt Oldring and Murrey Holmes were not offered terms.
Boss Howe told the Daily Echo: It's a really hard part of the job but we have made the decisions and are delighted for the three lads we have offered contracts.
I need everyone in my squad to be able to play because we won't be carrying a big squad again next season so it's up to these lads to grasp the opportunity.
Howe admitted it was difficult to tell the remaining six that there would be nothing on the table for them and added: In some senses, we want to be proved wrong because we want the lads to go on to have good careers.
Unfortunately, it's not going to be with us at this moment in time. But they are difficult decisions and nothing is ever clear-cut.
Meanwhile, the club has offered two-year scholarships to 10 players, including teenage striker Jayden Stockley, who has already featured for the first team this season.
Among the prospective new intake could be the sons of ex-Spurs star John Chiedozie and former Reading ace Michael Gilkes.
Strikers Jordan Chiedozie from New Milton and Harrison Gilkes from Reading have also been offered places.
The remaining seven are Ryan Case (Basingstoke), Clive Makoni (Southampton), Brad Strickland (Southampton), Josh Wakefield (Isle of Wight), Elliott Ward (Parkstone), Marco Zocchi (Jersey) and Alex Moth (Southampton).
Goalkeeper Gareth Stewart made a guest appearance and kept a clean sheet as Cherries drew 0-0 with Combination rivals Swindon Town yesterday.
Stewart, who works on the community side at Dean Court, was drafted in as a late replacement after Cherries had been refused permission to field a trialist.
Cherries gave a run-out to trialists Frank Danquah (Newcastle United), Curtis Wynter (Coventry City) and Antony Glover (Ebbsfleet).
Cherries: Stewart, Wynter, Cummings, Partington, Guyett, Hester (Stockley, h-t), Glover, Igoe, Goulding (Strugnell, 65), Danquah, McQuoid. Unused sub: Parsons.