A warranty or guarantee is predicated on the fact that the homeowner assumes responsibility to minimally provide water for the plantings. This is expressed or implied in any planting guarantee. Can you post what your guarantee says?
Like Stonehenge said, this is something that you should be paid for regardless of your lack of experience or wishful thinking. If you haven't already, you should discuss the issue with your client and not assume full responsibility for the replacements if the trees die due to lack of water. You should explain the situation and the options available to them (gator bags, water truck, fire truck, moisture retaining polymer, whatever) and let them know the various costs associated with each solution.
Some clients will agree with you and thank you for being on top of the issue and many clients will do the guilt thing and say, "well if you knew they needed water, why did you plant them so far away?" You can counter with "Why did you ask me to plant them so far away. Since everyone knows plants need water, how did you plan on keeping them watered?" (ixsnay the hoping for rain part, that won't help your argument). This puts it back in their court?
You absolutely cannot assume full responsibility to water the plants at your cost and than replace the trees at your cost. Let them pay for the watering solution so that you can maintain their warranty. I would talk to them in person and follow up with a nice reminder letter (that has a return receipt). It's OK to make mistakes, and learn from your mistakes, but you don't always have to pay for them.
For the future, I would tie the guarantee into your payment structure. We require full payment within 2 weeks of the completion of the project (or one week of billing date) otherwise all guarantees are null and void. Since our industry is silly enough to take responsibility for the plants, we should at least get paid in full as quickly as possible. This should be written in your contracts because it will hold up in court (assuming all work was completed as per contract).
If nothing else works you can always try this.
YouTube - IRD