The U.S. House can review the already-existing evidence for impeachment, such as in a debate on a vote for impeachment. But they cannot try to unearth grounds for impeachment that they do not already have
Subpoenas Not Valid Since There Is No Impeachment Inquiry
Here's some free legal advice: Trump Administration officials should reject the recent subpoenas by the House of Representatives Democrats. They read like political speeches, intended to influence public discussion, not like legal subpoenas. To answer these "when did you stop violating the law?" letters is to buy into and endorse their false premise.
If a Trump official were my client, I would recommend a short, quick letter in response. But would my client run the risk of not complying with a subpoena? Could officials who don't cooperate be found in contempt or be accused of obstruction of justice?