There is not a component within Luminate Online to delete gifts in bulk.  You can potentially compile all of the transaction id's in excel and use Excel functionality to create dynamic urls for each delete to make it easier.

For standard donations:
The url format for an offline donation delete will look like this:

The factors that will be unique for your site: 

Y = You can determine your secure number by looking at your admin url.
shortname= will be your site shortname
tx_id= will be the transaction id of the transaction you would like to delete.  Transaction id's are the last set of numbers in a user confirmation code.

A final url will look something like this:

For TeamRaiser donations:
Use the following URL that uses "del_tr_gift" rather than "del_offline". If you use the URL above for TR gifts, the gift will not be removed from the TR, only the donor's record. This will cause the TR amounts to be incorrect, and will require a Services engagement to correct the data.