I would say you can correctly convey the same meaning through both the sentences. And they both are grammatically correct. It is all about what is more common and what sounds good. Generally what sounds good is what is more common. So it is wise for a non native speaker especially learners to stick to that. In the rest of my answer I will try and show you exactly that.
CASE 1 - "time" in attributive position in a Compound Noun
regardless of time [NOUN] ... = 4
1. Now, regardless of time constraints, limited staffing or even a non-sales personality, you can reach out and touch virtually everyone vital to your success as often and as appropriately as you want.
regardless of the time [NOUN] ... = 8
1. Regardless of the time zone where you live, it's very late.
CASE 2 - "time" is being post modified by a past participle form of verb.
regardless of time + Past Participle form of Verb ... = 3
1. This confirms prior findings in research that regardless of time passed, trauma work -- such as working with suicidal clients -- can have long-lasting negative effects.
regardless of the time + Past Participle form of Verb ... = 2
1. The data shows that, regardless of the time elapsed between question and answer, virtually all of the English-speaking patients' questions were provided some form of an identifiable answer.
CASE 3 - "time" is used alone or coordinated
regardless of time ... = 11
1. Brennan isn't Dick Vermeil or Roy Williams, coaches who cry regardless of time or final score.
regardless of the time ... = 4
1. Tell Ross to call me the minute he gets home, regardless of the time.
2. If unanimity is not attained, the dissenters are likely to complain that the matter has been railroaded, regardless of the time and care that have been devoted to its consideration.
CASE 4 - "time" post-modified by a Preposition Phrase (PP)
POST-MODIFIED by "of" PP
regardless of the time of = 12
1. She and I were renting a damp and freezing little flat a couple of floors above two shops, a chip shop and a record shop, and the chip shop sent its lardy smell out regardless of the time of day, and the record shop seemed to play on repeat, the whole time we were breaking up (the whole time we went unspeaking up and down the cracked linoleum stairs, or one or other of us sat in the only privacy there was, behind the locked door of the outside toilet out on the staircase landing, where someone at some time or other had burned browncircle cigarette holes through the net curtain stuff hung over the back of the door), Bowie and Bing.
regardless of time of = 3
1. Numerous studies have demonstrated fatigue is related to the absolute number of hours driven regardless of time of day. For example, an Institute study found Washington state truck drivers behind the wheel for more than eight hours had a statistically significant twofold increase in crash risk.
POST-MODIFIED BY OTHER PP
regardless of time PP ... = 3
1. All incident cases of MS or other demyelinating diseases were also identified, regardless of time since exposure; cases occurring within 2 years of vaccination were compared with those occurring after 2 years in a self-controlled case series.
2. This model assumes that the relative risk is constant regardless of time from surgery.
3. Temporal patterns from 1987 and 1988-93 tagging show that the highest number of returns within southeast Florida occurred during the same season as tagging regardless of time at large, implying that there is a regrouping of some of the same fish each winter and spring in southeast Florida.
regardless of the time PP ... = 2
1. The wheelchair-to-knee excursion ratios were calculated in accordance with SAE J2249, using the peak excursion values of each variable, regardless of the time at which they occurred.
[The numbers indicate the number of occurrence in American Engliah Database]