お世話をかけます(おせわをかけます)
o-sewa wo kakemasu
This is a kind of idiomatic Japanese phrase, the kind that you should learn even if you don’t really understand what the parts mean individually. The literal connotation is something like “I am sorry to have to accept your generosity.” Basically though, it means “I’m sorry to trouble you.” It can even be translated as merely “Thank you for the help.”
“kakemasu” is the -masu form of the verb “kakeru” (can be used in many situations, from starting something to putting something on to making a phone call!)
“o” is an honorific, ie, a prefix attached to some words to make you sound more polite.
In this case, Esther is apologizing for having caused her host trouble due to her companion Abel clumsily falling into a pond in the garden and causing a mess….

Listen to Esther from Trinity Blood say “o-sewa wo kakemasu”
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o-sewa = (honorific)-help/caring
wo = particle marking the object
kakemasu = to wear, to put on, to begin to, to make a call, to play something…