Regarding finished past events, we use the
present perfect simple to relate events that occurred in a time period that has not yet finished
and the
simple past for events that took place in a time period that has ended.
American English generally allows for the use of either tense in these situations, while British English grammar insists on using the two tenses to distinguish them.
The arrest took place in the time period of "early this morning", which is apparently assumed to be over at the time of the utterance. So the relevant fact is not that the arrest is finished, but that the early morning is finished.
"This is the third time she's been arrested this year", on the other hand, occurs in an unfinished time period (if this year is not yet over), and so allows for (British: requires) the present perfect.
This is a case where both are grammatical, but express different concepts.
The past tense gives the sense that the efforts are in the past; there were specific efforts made, "my efforts" refers specifically to those efforts, and those efforts are no longer existing. An example would be "I tried to find the travel option with the smallest carbon footprint when I traveled to my relative's wedding". Travelling to the wedding was a one time thing that happened in the past, so past tense would be appropriate.
The present tense gives the sense that the efforts still apply in the present. This could be because the efforts are ongoing, still possible, etc. An example would be sorting recyclables out of the trash. If you are still currently doing this, then the present tense is appropriate. Even if you currently aren't doing it, one can still speak in the present tense of the effectiveness of it, if one treats the discussion as being about the general concept of sorting recyclables, rather than the specific acts that happened in the past.
One issue is whether "my efforts" refers to already determined efforts, or what efforts one does. That is, "My efforts are inadequate" has the primary meaning of "There are particular efforts that I made, and those efforts are inadequate", or it could mean "Whatever efforts I end up making, they will be inadequate". While the present tense can work for either, it works more for the latter.
Best Answer
With recently you could use either the Simple Past or the Present Perfect.
The Present Perfect is used:
The difference between I recently bought a mobile and I have recently bought a mobile is not that the latter describes an action that has been recently completed. The latter sentence describes an event that is still relevant at the present time, for example because you still have that mobile, and you didn't sell it, or you didn't replace it with a different one.